A practical guide to machine learning interatomic potentials -- Status and future

• The review addresses the difficulty nonexperts face in navigating the rapidly growing MLIP literature and provides a more in-depth practical perspective than briefer related overviews.It targets technically literate materials scientists and chemists with molecular-modeling backgrounds rather than MLIP specialists.Source: §1 · pp. 4–5
• It explains broad differences, benefits, and trade-offs among MLIP approaches such as atomic cluster expansion and graph neural networks while keeping deep mathematics and formalism to a minimum.The review focuses on the fundamental aspects needed to understand the MLIP landscape rather than technical details such as basis-function expansions.Source: §1 · p. 5
• The guide covers MLIP applications, general frameworks, fitting and pre-fitted workflows, speed and accuracy, and supporting infrastructure.These topics are presented as the key practical and conceptual aspects required to understand and use MLIPs.Source: §1 · p. 5
• The review surveys MLIP foundations and universal MLIPs, including their structures, formalisms, capabilities, downsides, and potential applications for organic and inorganic systems.It distinguishes explicit environment-featurization approaches from implicit graph-neural-network approaches and discusses recent advances in universal MLIPs.Source: §1 · p. 5
• Later sections provide practical guidance on execution speed and MLIP selection, infrastructure and training resources, limitations and mitigation strategies, and future developments over the next 3-10+ years.The discussion includes hardware, simulation size and time, energy and force accuracy, pre-trained versus newly fitted potentials, long-range interactions, magnetic systems, and excited states.Source: §1 · pp. 5–6

Purpose and scope

• The list standardizes names, acronyms, and citations for the MLIPs discussed in this paper, while explicitly excluding comprehensive coverage of all existing MLIPs.The listed methods span neural-network, graph, Gaussian-process, tensor, and cluster-expansion approaches, among others.Source: §2 · p. 6

Named MLIPs

• The supplied entries identify ANI, ACE, ænet, ALIGNN-FF, AIMNet2, and BP-NN [19] among the listed methods.Source: §2 · p. 6
• The cited entries include EquiformerV2-OMAT24, ACE with message passing (MACE), MACE foundation model (MACE-MP-0) [32], MACE-OFF23 potential for organics [33], Moment Tensor Potential (MTP), and PreFerred Potential (PFP).Source: §2 · pp. 6–7

• MLIPs map atomic positions and element types to total energies, typically providing analytical forces and, for periodic systems, stresses as derivatives of the potential energy surface.Some high-performing models instead train energies and forces separately, making them non-conservative.[24,30,36]Source: §3 · p. 7
• MLIPs bridge AIMD’s accuracy–scale limitation and physics-based potentials’ accuracy limitation, enabling large-scale simulations of specific materials with accuracy approaching AIMD.Parallel computing and frameworks such as LAMMPS, support simulations of large-scale emergent phenomena.Source: §3 · p. 8
• Compared with PBPs, MLIPs use flexible functional forms that can fit essentially arbitrarily complex atomistic energy landscapes and capture chemical changes when adequate training data are available.Their applicability is not fundamentally restricted to metallic, ionic, nonreactive, or other specific material classes, although present capabilities remain constrained.Source: §3 · pp. 9–10
• MLIPs typically achieve errors of a few to tens of meV/atom, often an order of magnitude better than typical PBPs.Their main costs are substantial training-data requirements and, depending on the model, higher computational expense; adding diverse training data can iteratively correct errors.Source: §3 · pp. 9–10
• MLIP MD could partially replace ab initio calculations for applications requiring energies and forces, making AIMD-like time and length scales accessible with orders of magnitude less compute time.This could unlock physical regimes inaccessible to AIMD and potentially replace much quantum-mechanics-based AIMD.[s3.p86#18e318]Source: §3 · pp. 10–11
• Growing evidence supports quantitative universal MLIPs that could provide almost instant access to broad chemical and structural spaces, directly or after fine-tuning.These models are envisioned as analogues of foundational models in computer vision and language machine learning.Source: §3 · p. 11

Capabilities

• MLIPs may deliver quantum-mechanical accuracy across almost any chemical system at scales of millions to billions of atoms and microsecond-or-longer timescales.[32]These capabilities could substantially expand molecular simulations.Source: §3 · p. 11

Scientific impact

• MLIPs could significantly enhance molecular simulations across chemistry, biology, materials science and engineering, physics, and other disciplines.The expected impact spans many fields of science.Source: §3 · p. 11

Accessibility and adoption

• Existing understanding, methods, and tools already enable non-experts to apply MLIPs to practical problems, supporting an expected expansion across scientific fields in the next few years.The review presents this accessibility as a basis for broader adoption.Source: §3 · p. 11

Remaining challenges

• Realizing MLIPs’ full potential still requires improved features and architectures, better training strategies, added physics such as long-range interactions, universal potentials, and robust solutions for complex systems.These challenges include both methodological refinement and successful scaling and adoption of potentials.Source: §3 · p. 11

4.1 The Basic Structure of an MLIP

• MLIPs generally represent each atom’s local environment with an atomic environment featurization (AEF), then use regression to predict properties; more expressive feature sets can improve accuracy.The model’s accuracy depends on how well the features and regression model capture local environments.Source: §4.1 · p. 12

4 Understanding the Types of MLIPs - Basic Formalisms

• Although categorizing MLIP approaches is challenging and their boundaries are becoming more nebulous as approaches converge, explicit versus implicit AEFs remain a helpful distinction at present.Source: §4.2 · p. 12

4.2 Explicit vs. Implicit MLIPs

• Explicit AEFs predefine element-specific features, whereas implicit AEFs learn atomic and bond embeddings; implicit methods are typically more architecturally complex and may be slower to train and execute.Implicit AEFs are commonly used for systems containing many elements because their learned features can scale more efficiently with chemical-species count.Source: §4.2 · pp. 12–13

4.3 Explicit AEF Type MLIPs

• Explicit AEFs encode local atomic densities with radial and angular basis functions, while symmetry-aware constructions enforce permutation, translation, and rotation behavior before ML prediction.Tensor products can produce covariant features, although scalar invariant features are also commonly passed to standard ML models.Source: §4.3 · p. 13
• Explicit AEF models are trained by mapping local-environment arrays to energies, forces, and stresses using regression targets typically obtained from large ab initio datasets such as DFT.Useful configurations include stable structures, relaxation structures, and AIMD snapshots.Source: Figure 2 · p. 14, §4.3 · p. 14
• Fitting commonly combines force-derivative and whole-configuration energy terms, with loss functions extendable to stresses, virials, polarizabilities, and other properties.Some neural-network MLIPs omit forces during training but can recover comparable accuracy with larger datasets.Source: §4.3 · pp. 14–15
• The main regression choices trade fitting and execution speed against accuracy: linear regression is simplest and fastest, GPR is intermediate, and neural networks are most complex, slowest, and generally most accurate.For small datasets, GPR can exceed neural-network accuracy, while its fitting speed depends strongly on dataset size.Source: §4.3 · p. 15
• Explicit AEF MLIPs combine engineered atomic-environment features with regression models, but no single model is universally best and continuous predictions are required.Examples include ACSF with neural networks, SOAP with sparse GPR, and HBFs, MTFs, or ACE with linear regression.Source: §4.3 · p. 15
• ACE conceptually contains ACSFs, SOAP, HBFs, and MTFs as special cases, while earlier feature choices can remain advantageous for training or execution efficiency.Different AEFs can also be paired with different regression models.Source: §4.3 · p. 16
• For explicit AEFs, a body order of v+1 yields O((N_b⨯S)^v) basis functions, producing quadratic scaling for body order 3 and often limiting models to approximately 5 or fewer species.Here N_b is the number of basis functions per chemical element and S is the number of elements.Source: §4.3 · p. 16

4.4 Implicit AEF and GNN MLIPs

• Implicit AEFs address explicit chemical scaling by learning feature-vector embeddings that represent different chemistries without explicitly constructing basis functions for each element.The approach dramatically reduces the complexity of treating different elements, although the precise reason is not fully clear.Source: §4.4 · p. 16
• DeepMD learns coordinate-dependent embeddings from local distances, angles, and atom types, allowing it to fit many elements; related compression methods include element vectors demonstrated for up to 11 species[16].Linear embedding formally corresponds to tensor decomposition and converges toward the uncompressed result as embedding dimension increases.Source: §4.4 · p. 17
• GNNs represent atoms as nodes and near-neighbor interactions as edges, iteratively updating learned node and edge embeddings to encode local chemistry and structure.Equivariant GNNs preserve appropriate symmetries and appear particularly data-efficient in fitting.Source: §4.4 · p. 17
• GNN message passing can couple atoms 3-4 nm apart, helping capture medium-range interactions but creating memory and parallelization issues; local alternatives such as Allegro[13] and MACE show excellent scalability.MACE uses high-body-order local features so that only two graph hops can suffice for convergence.Source: §4.4 · p. 18

4.5 Unifying explicit and implicit AEFs

• Explicit and implicit AEFs are increasingly viewed as different aspects of a single general MLIP approach, despite having developed largely independently.The supplied passage begins this unifying perspective by contrasting explicit AEFs’ focus on local descriptions of atomic energy with implicit approaches.Source: §4.5 · p. 18
• Implicit AEF message passing propagates information beyond one cutoff distance by assembling local-environment messages and using them to compute another atom’s energy.This changes neighboring atoms from being characterized only by positions and elements to carrying environment-dependent attributes.Source: §4.5 · pp. 18–19
• In implicit AEFs, neighboring atoms acquire attributes from their environments; equivariant networks represent these attributes as vectors and tensors, producing an environmentally dependent, non-spherical character.For example, the same carbon atom can differ between a surface and the bulk.Source: §4.5 · p. 19
• ACE provides a complete local-environment basis and formally complete messages when applied to neighboring atoms, while recursive ACE yields multi-ACE implicit constructions.[59]The general graph-basis perspective underlying grACE uses ACE-like star graphs and linear combinations of graph-defined basis functions.Source: §4.5 · p. 19
• Enumerating general graph basis functions scales exponentially with graph nodes or edges, motivating iterative tensor-decomposition evaluation along the ACE basis.[59]This efficient evaluation corresponds to tree graphs and is equivalent to message passing in models such as NequIP and MACE.Source: §4.5 · p. 19
• Explicit AEFs with tree-structured graphs and at least two layers can be transformed into implicitly represented AEFs, yielding message-passing neural networks for efficient evaluation.Single-layer explicit AEFs are also often evaluated iteratively by body order for numerical efficiency.Source: §4.5 · p. 19
• The explicit–implicit distinction primarily reflects AEF development history and implementation details rather than different mathematical structures.All AEFs can be represented explicitly, whereas iterative evaluation for numerical efficiency produces implicit representations.Source: §4.5 · p. 19
• Current results suggest convergence toward a single general MLIP formalism, in which apparently different approaches are specific choices within one design space.This perspective may help identify methods jointly optimized for training efficiency, prediction speed, and accuracy.Source: §4.5 · pp. 19–20

Definitions

• Targeted MLIPs typically cover about 1–10 elements under chemical, structural, or phase constraints, whereas universal MLIPs target roughly 10–100 elements with fewer restrictions.Universal MLIPs become more useful as they include more elements and permit a wider range of chemical or material structures.Source: §5 · p. 20
• Semi-universal MLIPs focus on selected domains, while true U-MLIPs aim to represent most chemically relevant elements in solids, liquids, and molecular structures.The categories are approximate; U-MLIPs generally require scalable implicit AEF methods and sufficiently large, diverse training data for useful accuracy across compositions and structures.Source: §5 · pp. 20–21

Semi-universal examples

• Examples of semi-universal potentials include AIMNet2 for up to 14 elements, Elemental-SDNNFF for Heusler alloys containing 55 elements, and SuperSalt for molten salts with 11 cations.Elemental-SDNNFF predicts accurate forces and phonon properties, while SuperSalt was significantly more accurate than existing U-MLIPs for its target materials.Source: §5 · p. 21

Broad U-MLIPs

• MACE-MP0, trained on publicly available data also used by CHGNet and SevenNet, demonstrated high accuracy in three illustrative molecular-dynamics applications and stable simulations lasting many nanoseconds.The section defines U-MLIPs loosely as models trained on sufficiently large and diverse datasets to provide usefully accurate predictions across wide compositional and structural ranges.Source: §5 · pp. 21, 23

Organic SU-MLIPs

• Organic SU-MLIPs progressed from ANI to AIMNet2 and MACE-OFF3, adding broader elemental coverage, charged and valence-state treatment, or improved benchmark molecular-simulation performance.AIMNet2 includes short-range van der Waals and long-range electrostatic corrections; ANI-1xnr also models organic liquids, supercritical fluids, and chemical reactions.Source: §5 · p. 22

Broad U-MLIPs

• The first published U-MLIPs intended to have broad applicability across most elements include M3GNet, CHGNet, ALIGNN-FF, PFP, and GNoME.Source: §5 · pp. 22–23

Efficiency

• Orb achieves MatBench-leading performance with faster execution than other leading universal MLIPs, running 3-6 times faster than PyTorch MACE before custom CUDA kernels remove the advantage.The speed advantage is especially relevant for large systems and when dispersion corrections are included.Source: §5 · p. 23

Benchmark interpretation

• Thermal-conductivity performance can diverge from MatBench stability rankings, with MACE outperforming other models by a substantial margin.This cautions against extrapolating general performance from energy-sensitive benchmarks alone.Source: §5 · pp. 23–24

Model architecture

• Universal MLIPs extend graph models with physically informed energy dependencies, enabling forces and stresses through differentiation and incorporating multi-body interactions, coordinates, and lattice information.M3GNet uses three-body interactions for computational efficiency, while ALIGNN-FF predicts atomwise and gradient quantities for forces and stresses.Source: §5 · p. 25

Training data

• Training databases for universal MLIPs grew by more than an order of magnitude annually, from roughly 2⨯10^5 configurations in 2022 to 1.18⨯10^8 in 2024.Continuing this trend could yield billion-calculation databases and potentially further performance improvements.Source: §5 · p. 25

Performance and applicability

• Universal MLIPs accurately model diverse materials phenomena, generally surpassing EAM-like potentials and approaching explicit local-environment methods, with prospects for near-DFT accuracy.The reported comparisons are not directly comparable because models use different training and testing databases.Source: §5 · p. 28

Magnetic and charge effects

• CHGNet embeds magnetic moments in atomic representations for charge-informed simulations, reducing energy, force, and stress errors by 1-10% compared with omitting magnetic moments.Its outputs include energies, forces, stresses, and per-atom magnetic moments, supporting phenomena correlated with charge states.Source: §5 · p. 28

• CHGNet accurately distinguishes transition-metal valence states and models charge transfer, charge-coupled degradation, and electronic-entropy-driven phase stability in battery materials.It reproduces the qualitative Li_xFePO_4 miscibility gap when Fe valence effects are included, whereas omitting them removes the gap.Source: §5 · p. 29
• 81 meV/atom was CHGNet’s formation-energy MAE, while CHGNet and MACE-MP0 best converged cell relaxations and MACE-MP0 best predicted vibrational properties.[73]M3GNet had numerous non-converged full-volume relaxations, and ALIGNN-FF showed qualitative phonon-band errors.Source: §5 · p. 29
• 0.67 (MACE-MP0) > 0.61 (CHGNet) > 0.57 (M3GNet) > (everything else) were stable-material classification F1 scores, with MACE-MP0 performing best.[76]MACE-MP0 and CHGNet each achieved 60 meV/atom convex-hull-energy MAE, and all three U-MLIPs outperformed other models.Source: §5 · p. 30
• None of M3GNet, CHGNet, or MACE-MP0 accurately reproduced metallic-binary-alloy mixing energies in adequate agreement with DFT.U-MLIPs systematically soften the potential-energy surface, producing underpredicted energies and forces, likely because training configurations cluster near relaxed minima.Source: §5 · p. 30
• Benchmarking should assess physically relevant properties such as surface, defect, and mixing energies, phonons, and elastic constants rather than only energy and force errors.CHIPS-FF provides open-source infrastructure for benchmarking U-MLIP materials properties, while test-set design must avoid overfitting one property at the expense of others.Source: §5 · p. 31
• Surface-energy errors are substantially larger than bulk-energy errors because surfaces were absent from training, with M3GNet and CHGNet underpredicting and MACE-MP0 sometimes overpredicting.[74]Targeted MTP and NequIP models can reduce errors for specific systems but sacrifice zero-shot generality.Source: §5 · pp. 29–30, Figure 5 · p. 32
• Fine-tuning pretrained U-MLIPs alters only a small fraction of weights, requires less data than fitting from scratch, and can yield lower downstream errors.Preconditioned weights support focused models for specific chemical or structural families, and fine-tuned error improves with pretraining-data size according to a power law.Source: §5 · p. 33

Use cases

• U-MLIPs could reduce DFT relaxation time by a factor of three, with inaccuracies largely mitigated because the final result comes from a full ab initio calculation.This use case could become standard practice and reduce ab initio calculation time across potentially billions of future calculations.Source: §5 · p. 33
• U-MLIPs can replace or expand AIMD by enabling large-scale, long-time simulations and materials exploration across chemically and structurally complex multicomponent systems.Their broad applicability supports screening properties such as Li-ion conductivity and elastic modulus without the scaling issues of many-component systems.Source: §5 · pp. 33–34

Materials exploration

• Screening materials properties across the periodic table, previously possible only with computationally expensive ab initio calculations, could be made roughly 1000⨯ faster.Matterverse.ai is described as a Materials Project-like repository containing millions of hypothetical structures generated using physics-based considerations.Source: §5 · p. 34
• Combining generative inverse-design models with U-MLIPs may enable fast discovery of exceptional materials beyond conventional screening approaches [82] [83] [84] [87].Candidate tools include CDVAE, MatterGen, SHAFT, UniMat, and large language models for stable crystal generation.Source: §5 · p. 34

Limitations

• U-MLIPs have uncertain domain applicability, may contain unpredictable major weaknesses, and are generally slower than targeted MLIPs.A model might accurately predict Li-diffusion properties for 95% of solid electrolytes yet be substantially inaccurate for the remaining 5%.Source: §5 · p. 34

Future outlook

• Centralized U-MLIP development could integrate long-range forces, speed optimizations, multifidelity learning, fine-tuning, and uncertainty quantification into shared models.A single potential with near ab initio accuracy, much greater speed, broad elemental coverage, and increasingly complex physics could become a foundational model for materials modeling without explicit training.Source: §5 · p. 35

Benchmarking caveats

• Timing values are qualitative guides because hardware, hyperparameters, software optimizations, and system size strongly affect results, so projects concerned with speed should benchmark current package versions directly.Model complexity can change approximate timing by an order of magnitude, and larger systems can improve processor utilization; reported values are rounded and based on representative state-of-the-art hardware.Source: §6 · p. 35

Benchmarking metric

• Processor-seconds per atom per step enables comparisons across atom counts, processor counts, and multistep simulations when each processor handles sufficiently many atoms.Single-processor results are reported in s/atom/step, while larger parallel runs incur MPI communication overhead; the metric is largely insensitive to system and processor counts in the linear-scaling regime.Source: §6 · p. 36

Explicit AEF MLIPs

• 10^-5 to 10^-3 s/atom/step covers well-fit explicit AEF MLIPs, with faster MTP and ACE models typically near 10^-4 s/atom/step.In 1024-atom Cu_xAl_1-x cells, ACE took 0.06×10^-3–0.18×10^-3 s/atom/step, GAP took 2.1×10^-3, and MACE took 0.042×10^-3–0.12×10^-3 on a single A100 GPU.Source: §6 · pp. 36–37, Figure 6 · p. 37

Deep-learning and universal MLIPs

• Deep-learning MLIPs are generally similar to or somewhat slower than explicit AEF approaches, although DeepMD improved from about 10^-3 proc-s/atom/step on CPU to about 10^-4 on GPU, a ~40-fold acceleration.The PFP U-MLIP ran at about 10^-3 s/atom/step on a GPU and was about five times slower than identical single-CPU MTP and ACE runs and 50–100 times slower than large CPU sets.Source: §6 · pp. 37–38

Ultra-fast potentials

• 10^-6 s/atom/step is achievable with ultra-fast spline-and-linear-regression potentials, about 10^3 times faster than typical explicit AEF MLIPs but with limited flexibility and potentially larger errors.These models matched SNAP, GAP, and MTP accuracy on some test cases and were comparable to the fastest simple physics-based potentials.Source: §6 · p. 38

Large-scale parallel execution

• DeepMD achieved 10^-5 proc-s/atom/step with about 127 million Cu atoms, while SNAP achieved 10^-6 with about 20 billion C atoms, both running on 27,900 GPUs.FLARE modeled heterogeneous catalysis of H2/Pt(111) for 0.5 trillion atoms on 27,336 GPUs, achieving 10^-6 proc-s/atom/step; on CPUs, it reached roughly 10^-3 proc-s/atom/step.Source: §6 · pp. 38–39

Large-scale execution

• Some MLIPs can scale to even hundreds of billions of atoms, but these calculations generally require multiple GPUs that may be challenging to access.Options for accessing suitable infrastructure are becoming increasingly available.Source: §6 · p. 39

Speed trends

• Simple PBPs remain fastest, followed by explicit AEF MLIPs and then implicit AEF deep-learning MLIPs in larger-scale calculations.This preserves the general speed trend observed on one CPU.Source: §6 · p. 39

Method selection

• MLIP fitting and optimization details can strongly affect large-scale calculation performance, so studies should select the approach carefully.The optimal choice depends on the specific fit and optimization used.Source: §6 · p. 39

• MLIP selection should consider multiple factors rather than a single criterion.The section introduces guidance for thinking through these factors when choosing MLIPs.Source: §7 · p. 39
• The discussion begins with hardware, accuracy, and speed as basic considerations.Source: §7 · p. 39
• It then progresses to details relevant to pursuing a specific application.Source: §7 · p. 39

7.1 Hardware Resources

• Explicit AEF MLIPs such as MTP, ACE, SNAP, and GAP generally have fewer parameters and run well on CPUs, while NN- and GNN-based MLIPs mostly rely on GPUs.MTP currently runs only on CPUs; ACE is faster to fit on GPUs but supports MD simulations on both CPUs and GPUs.Source: §7.1 · pp. 39–40
• NN-based MLIPs can run on CPUs but typically incur a 10-100⨯ slowdown relative to GPU calculations.They are primarily designed for fitting and use with GPUs.Source: §7.1 · p. 40
• CPU-only users should generally favor explicit AEF MLIPs, whereas GPU access makes both explicit AEF and NN-based MLIPs potentially suitable choices.Because U-MLIPs and many MLIP workflows increasingly use GPUs, extensive users are advised to have at least one high-performing GPU.Source: §7.1 · p. 40
• Matlantis provides PFP inference through a SaaS API, with execution handled by backend GPUs or MN-Core deep-learning accelerators, so users need not manage computing environments or device optimization.This commercial deployment abstracts the hardware requirements of inference from the user.Source: §7.1 · p. 40

• Simulation time depends on system size, execution steps, available hardware resources, and the MLIP’s computational cost.Source: §7.2 · p. 40
• Explicit AEF MLIPs are about 10-100⨯ faster than implicit AEF deep learning MLIPs when project and infrastructure factors are fixed.Source: §7.2 · p. 40
• When computational cost is not limiting, users may choose deep learning MLIPs for their typically highest accuracy; otherwise, explicit AEF MLIPs are alternatives.Source: §7.2 · p. 40

Accuracy limits and model formalisms

• Earlier MLIPs were limited by incomplete three- and four-body descriptions of local atomic environments, whereas MTP and ACE use systematically improvable high-body-order basis functions with linear regression.These formalisms improve accuracy while keeping computational cost tractable.Source: §7.3 · p. 41

Hardware-dependent recommendations

• Equivariant GNNs—including NequIP, Allegro, TeaNet, SO3krates[99], and MACE—can achieve very high accuracy at practical computational cost, especially when GPUs are available.The authors recommend these models when GPU resources permit training.Source: §7.3 · p. 41

Training strategy

• Fine-tuning a pre-trained potential can yield higher accuracy than training a new MLIP from scratch, including for tasks out of distribution relative to the training data.This recommendation is based on reported findings and the authors’ experience.Source: §7.3 · p. 41

Empirical accuracy comparison

• With abundant training data, ACE tends to have energy and force RMSEs 2-3 times those of GNN methods such as MACE in the authors’ experience.This comparison assumes that additional DFT data can be generated until further potential improvement is small.Source: §7.3 · p. 41

Hardware-dependent recommendations

• If only CPUs are available, the authors currently suggest MTP or ACE, while anticipating rapid changes as implementations improve and diversify across hardware.The recommendation reflects the current inefficiency of GNN packages on CPUs.Source: §7.3 · p. 41

7.4 Using A Pre-trained Potential

• Pre-trained potentials are available through online repositories and scientific articles, including targeted models in the NIST Interatomic Potentials Repository and OpenKIM.Source: §7.4 · p. 41
• U-MLIPs are easy to import and broadly applicable, but low energy and force errors do not ensure accurate materials properties, which remain insufficiently validated across most systems.U-MLIPs may also be slower than other MLIP or PBP approaches, so speed requirements should be considered.Source: §7.4 · pp. 41–42
• Validate predicted energies and forces against consistent ab initio calculations, then compare target properties such as phonons, diffusion coefficients, or defect formation energies.Agreement on target properties provides greater confidence than agreement on energies and forces for selected structures alone.Source: §7.4 · p. 42
• Approximately 3⨯ time savings resulted when hypothetical structures were pre-relaxed with M3GNet before ab initio calculations.Pre-relaxation and initial candidate screening are failure-tolerant uses when later ab initio calculations can identify errors or refine results.Source: §7.4 · p. 43
• Because U-MLIP applicability remains uncertain, practitioners often use material-specific potentials or fit new ones, although some early adopters perform simulations without fine-tuning, including Matlantis PFP.Source: §7.4 · p. 43
• A pre-trained potential should match the study’s atomic structures, chemical states, and relevant physics; models trained on crystalline phases, low-valence states, or DFT-PBE may fail for other regimes.Examples include amorphous phases, high-valence transition metals, and systems where van der Waals interactions are significant.Source: §7.4 · pp. 43–44

7.5.1 Basic ideas

• A typical workflow generates application-relevant ab initio configurations, fits on about 80%, tests on the remainder, and iteratively adds data when energy or force errors are inadequate.Configurations may come from domain intuition, molecular-dynamics trajectories, active learning, or combinations thereof; GNN training commonly uses 80% training, 10% validation, and 10% testing.Source: §7.5.1 · p. 45

7.5.2 Determination of test data

• Validation data must reflect deployment conditions: random cross-validation is suitable for uncorrelated data but can be overly optimistic for correlated configurations because of the “twin” problem.For correlated data, assess new temperatures, later trajectory times, or expected use cases by comparing MLIP and ab initio energies and forces, while recognizing that property validation is costly and often has few comparison values.Source: §7.5.2 · p. 46

7.5.3 Required energy and force accuracy

• Required energy and force accuracy has no universal threshold: it varies with explored conditions, chemical and structural diversity, MLIP type, and the properties of interest.Typical very-good fits report 1–10 meV/atom energy and 20–40 meV/Å force errors, but low energy, force, and stress errors alone may not ensure accurate property predictions.Source: §7.5.3 · p. 47
• Low aggregate RMSE can still miss important outliers, such as activated Li-hopping states, producing inaccurate diffusion coefficients and poor transfer across environments.DeepMD reproduces liquid bulk-water properties less accurately at vapor–liquid equilibrium, illustrating that interpolation-like performance does not guarantee reliable predictions elsewhere.Source: §7.5.3 · p. 48
• Stable long-time MD requires more than small RMSE because inaccurate forces can accumulate numerical errors and cause simulations to crash.Stability can be improved by progressively diversifying training data, adding ab initio calculations from configurations preceding instabilities, and using domain-based active-learning approaches; typically no more than 5 iterations are needed.Source: §7.5.3 · pp. 48–49

7.5.4 Determination of training data, use of active learning

• Training databases should be diverse, relevant, and large; intuitive structure selection is practical and often yields a good MLIP quickly, but is difficult to automate and scale broadly.Data should include configurations tied to the target property, such as activated hops for diffusion and varied stresses for bulk moduli, while evaluation should include relevant rare-event metrics.Source: §7.5.3 · p. 48, §7.5.4 · pp. 49–50
• Active learning uses uncertainty-guided sampling and ground-truth calculations to add informative configurations, improving predictability and training efficiency.For FLiBe salts, active learning achieved about the same prediction error with less than half as many structures as intuitive selection (600 vs. 1400), while other comparisons found lower RMSE than random sampling.Source: §7.5.4 · pp. 50–51
• Bias potentials generate low- and high-energy configurations while avoiding unnecessary structural distortions, making them efficient for adding weakly correlated training data.They were combined with querying by committee and metadynamics to model proton phase-space transfer in glycine.Source: §7.5.4 · p. 51
• A SNAP MLIP workflow using principal component analysis for structure selection and differential evolution for hyperparameters achieved close to DFT accuracy for Mo properties.The reported properties included elastic constants, melting point, and surface and grain-boundary energies.Source: §7.5.4 · p. 51
• On-the-fly DFT queries triggered by excessive GPR error bars for Al diffusion were concentrated near the start of MD, with none after 400 ps.This FLARE workflow targeted vacancy and adatom diffusion in Al.Source: §7.5.4 · p. 51
• Classical PBP or U-MLIP trajectories can provide large initial configuration pools, which active learning or clustering can sample for ab initio training calculations.Clustering groups configurations by similar features and selects representatives; rare-event sampling can be integrated with active learning to describe rare events.Source: §7.5.4 · p. 52

7.6.1 Chemical Complexity

• 7.6.1 Chemical Complexity: Explicit AEF MLIPs scale quadratically with species, limiting FLARE offline fitting from about 4000 frames for one species to about 150 for five species.A 12-species ACE fit with 3500 training data failed to start on an Nvidia Tesla V100-32 GB GPU; similar issues affect MTP, ACE, and other explicit AEF MLIPs.Source: §7.6.1 · pp. 52–53

7.6.2 Training Requirements

• 7.6.2 Training Requirements: MTP fitted molten-salt FLiBe with less than 1% of DeepMD’s data, while NequIP studies report a 1000⨯ improvement over DeepMD in data requirements.The MTP–DeepMD comparison was not head-to-head under identical conditions and is therefore only a qualitative guide; newer equivariant deep-learning MLIPs are described as more data-efficient than early deep-learning models.Source: §7.6.2 · p. 53

7.6.3 Ease of Fitting (Tools and Hyperparameters)

• 7.6.3 Ease of Fitting (Tools and Hyperparameters): MTP is relatively easy to fit with one hyperparameter, whereas ACE and Allegro require more expertise and optimization.MTP lacked GPU training as of early 2024, and hyperparameter optimization can increase total fitting time by a few multiples, though automation may reduce this burden.Source: §7.6.3 · pp. 53–54

Potential choice

• For fast simulations or CPU-only workflows, explicit AEF potentials are recommended, particularly MTP for ease of fitting and ACE for accuracy.For slower workloads or GPU-equipped users, deep-learning potentials are practical but not necessarily required or optimal.Source: §7.7 · p. 54
• MTP is a strong default because it was highly accurate and fast, generally outperforming GAP, SNAP, and Behler-Parrinello NN potentials.The comparison supports starting with MTP when no more specific information is available.Source: §7.7 · p. 55
• ACE is a flexible method of choice because many explicit AEF basis functions are its special cases, but its flexibility increases hyperparameter complexity.The review also favors more complete potentials such as MTP and ACE over older forms such as SNAP when accuracy is important.Source: §7.7 · pp. 54–55

Pre-trained and reused potentials

• Pre-trained or reused targeted MLIPs can avoid training that typically takes days to months, but users should vet and validate them for the intended application.U-MLIPs are useful starting points when workflows include post-calculation checking, while reused models may differ from their original evaluation settings.Source: §7.7 · p. 55

Fitting new potentials

• When fitting new models, deep-learning potentials are generally needed beyond ~5 elements but require more data, training time, and hyperparameter-optimization effort.Recent methodological developments may remove the stated element-count constraint.Source: §7.7 · p. 55

Data platforms

• ColabFit Exchange curates nearly 400 datasets containing more than 230 million unique atomic arrangements for fitting MLIPs.The platform is tailored to advanced materials and chemistry applications and hosts curated, publication-derived training data.Source: §8 · p. 56

Fitting and verification

• KLIFF supports general-purpose fitting, OpenKIM deployment through LAMMPS, automated property testing, potential archiving, and uncertainty quantification.These capabilities support model verification and assessment of prediction reliability.Source: §8 · p. 56

Deployment platforms

• Garden packages containerized models with structured data, benchmarks, tests, and computing resources for consistent deployment across local machines, clouds, and HPC clusters.Its Globus Compute integration simplifies model discovery and execution across heterogeneous platforms.Source: §8 · p. 56

Simulation software

• LAMMPS remains a widely used MLIP simulation environment, while ASE supports molecular dynamics, energy and force calculations, and MLIP testing; newer models also integrate natively with JAX-MD.U-MLIPs including M3GNet, CHGNet, MACE-MP0, and EquiformerV2-OMAT24 can be loaded through ASE for relaxations or MD with a few Python lines.Source: §8 · pp. 56–57

Computing resources

• Many MLIPs require GPUs, and although access to 1-10 GPUs is increasingly common, large studies may require DOE or NSF facilities or cloud providers offering pay-as-you-go access.Garden standardizes deployment across local machines, national facilities, and cloud resources through Globus Compute.Source: §8 · p. 57

9 Limits of Standard MLIPs and Advanced MLIPs to Overcome Those Limits

• Standard MLIPs struggle with long-range forces, magnetic states, and electronic excitations, motivating advanced models that incorporate additional physics.The review emphasizes that these extensions are more difficult than simply increasing training data.Source: §9 · p. 58

9.1 Long-range interactions

• Local descriptors typically cover only 5–10 Å, so short-range MLIPs can miss electrostatic and dispersion effects that govern some properties.Complete long-range electrostatics may be necessary for higher-energy states lacking strong local charge neutrality.Source: §9.1 · p. 58
• Short-range representations can succeed for molten salts because screening and local charge neutrality suppress longer-range effects, but this success may not extend to higher-energy states.States without strong local charge neutrality require particular caution and potentially more complete electrostatic treatments.Source: §9.1 · pp. 58–59
• Long-range effects can be modeled explicitly with physics-based terms: DeepPot and SCFNN use Wannier centers, while AIMNet2 adds DFT-D3 van der Waals and electrostatic corrections.[18,144]SCFNN’s iterative refinement accurately predicts water’s high-frequency dielectric constant, and AIMNet2 extends to neutral and charged organic compounds.Source: §9.1 · pp. 59–60
• Global sGDML representations capture chemical interactions and long-range forces, but their all-pair correlations make them molecule-specific and non-transferable.Global representations can reduce computational complexity and improve training and simulation efficiency for small systems with significant long-range interactions.Source: §9.1 · p. 60

9.2 Modeling Systems Off the Born-Oppenheimer Surface

• Standard MLIPs assume a unique position-to-energy mapping; moving between Born–Oppenheimer surfaces therefore requires major formal changes, especially for magnetism and electronic excitation.Fixed excitations can instead be handled by training on the corresponding constrained Born–Oppenheimer surface.Source: §9.2 · p. 61

9.2.1 Magnetism

• Magnetic MLIPs must distinguish ions with different spin states and incorporate spin degrees of freedom, a difficult unresolved requirement for finite-temperature magnetic materials.Different magnetic states have substantially different properties, and no unique solution for differentiating spin states has emerged in the MLIP community.Source: §9.2.1 · p. 61
• Magnetic MLIPs have not yet achieved transferable, quantitatively accurate descriptions across different crystal systems, despite methods incorporating spin, vectorial fields, and magnetic moments.Existing approaches include Heisenberg-based models, non-collinear extensions, and atomic magnetic-moment prediction, but several remain restricted to collinear configurations or omit lattice information.Source: §9.2.1 · p. 62
• Non-collinear magnetic ACE for iron accurately reproduces ground-state properties across magnetic phases and captures magnetic and lattice excitations relevant to finite-temperature and defect behavior.[166]The model was trained on diverse collinear and non-collinear structures computed using SDFT.Source: §9.2.1 · pp. 62–63
• TENN-e3 incorporates time-reversal E(3) equivariance, spin-orbit effects, and collinear or non-collinear moments to model complex spin-lattice coupling and construct magnetic Hamiltonians.TENN supports extended-time-scale spin-lattice dynamics and large-scale magnetic-material electronic-structure calculations, while magnetic multicomponent applications still require efficient reference-data sampling and broader testing.Source: §9.2.1 · p. 63

9.2.2 Excited states

• No well-established MLIP currently exists for excited systems, whose modeling requires multiple excited-state PESs, forces, nonadiabatic and spin-orbit couplings, and substantially more complex training data.The underlying quantum-chemistry calculations and model complexity make excited-state MLIPs significantly more challenging than ground-state models.Source: §9.2.2 · p. 64
• The framework supports phase-free training, rotationally covariant nonadiabatic couplings, spin-orbit couplings, and simultaneous handling of different states with the same spin multiplicity.Source: §9.2.2 · p. 64
• The excited-state potentials are implemented as derivatives of virtual properties constructed by a deep neural network.Source: §9.2.2 · p. 65
• FIREANN introduces pseudo atomic field vectors with rigorous rotational equivariance, enabling prediction of multiple polarization response properties for accurately capturing excited-state PESs.The approach extends an embedded-atom neural network into a universal field-induced recursively embedded atom neural network.Source: §9.2.2 · p. 65

Near-term methodological advances

• Active-learning methods are expected to yield new ways to determine optimal training structures, including for complex chemical applications such as bond breaking and formation, while improving explicit AEF MLIPs based on GAP and deep learning MLIPs.Source: §10 · p. 65
• MLIP development is expected to shift toward faster, more automated fitting and evaluation, larger datasets, and standard treatments for long-range forces, magnetic states, and excited states.Magnetic methods such as non-collinear magnetic ACE and TENN may become standard in fitting packages, while more general excited-state methods may become widely accessible within 3–5 years.Source: §10 · p. 66

Infrastructure and adoption

• MLIP infrastructure is expected to become more integrated and accessible through multi-potential fitting, automated quality assessment, searchable repositories, FAIR practices, and application-specific recommendation systems.These developments aim to simplify model publishing, discovery, deployment, reproducibility, and informed package selection.Source: §10 · p. 67

Computing hardware

• Hardware portability will increasingly influence MLIP choice, because GPU acceleration favors large-scale simulations and users need models that perform well on available hardware.Performance-portable implementations such as Kokkos- and PyTorch-based MLIPs are favored, while new hardware could substantially expand molecular-dynamics capabilities.Source: §10 · pp. 67–68

Universal MLIPs

• In the 5–10-year horizon, universal MLIPs are identified as a particularly promising direction, analogous to foundational models that support adaptation across many specific applications.The comparison is motivated by foundational models’ broad task performance and utility in image generation and natural-language processing.Source: §10 · p. 68

• Universal MLIPs are progressing from qualitative or semi-quantitative screening toward quantitative modeling of specific properties and may eventually enable simulations beyond 1 ms.They are expected to increasingly replace targeted MLIPs and model phenomena inaccessible to current MLIPs.Source: §10 · p. 68
• Larger, more diverse, higher-fidelity and multifidelity datasets, faster hardware, improved algorithms, and model distillation are expected to support more accurate and application-specific MLIPs.Multifidelity training may help approach chemical accuracy (1 kcal/mol) and mitigate limitations of lower-fidelity DFT data, while distillation can derive fast models from slower U-MLIPs [81,181,182].Source: §10 · pp. 68–69
• The scale of future U-MLIP data and models may require hosting by a few resource-rich organizations, with infrastructure enabling model use, fine-tuning, distillation, and deployment across environments.Frameworks such as Garden [137,138] are beginning to connect models with distributed computing resources, analogous to APIs supporting large language models.Source: §10 · p. 69
• Semi-universal MLIPs covering intermediate element counts or restricted material classes may be more practical than full U-MLIPs because they simplify compositional and structural complexity.This approach can bridge models for a few species under limited conditions and models covering the full periodic table under all conditions.Source: §10 · pp. 69–70
• MLIPs may substantially reduce ab initio molecular-dynamics time and modeling energy requirements, although increased MLIP use could offset these savings and raise overall simulation utilization.Source: §10 · p. 70
• The future status of traditional potentials is unclear: AMBER potentials for many organic systems are close to chemical accuracy and very fast, while MLIPs can map positions beyond energies and forces.Yu et al. described fitting pair potentials with ML and converting them to simple Buckingham form, achieving almost optimal pair potentials.Source: §10 · p. 70