Source-linked AI summary
Data-Driven Collective Variables for Enhanced Sampling
Luigi Bonati, Valerio Rizzi, Michele Parrinello
TL;DR
Choosing collective variables is difficult when systems are complex and transition pathways are unknown. The paper uses neural networks with an LDA objective to compress descriptors from metastable states into collective variables, which draw paths through descriptor space and can promote transitions between those states.
Problem
Choosing collective variables that capture hard-to-sample modes is nontrivial for complex systems whose transition pathways are unknown.
Source: p. 2Method
Deep-LDA uses a neural network to compress descriptors from metastable states and maximizes an LDA objective to produce discriminative collective variables.
Source: p. 3, Aldol reaction · p. 8Results
Deep-LDA draws paths in descriptor space that are intended to promote transitions between metastable states using limited information.
Source: Aldol reaction · p. 8Takeaways & Limitations
Feature analysis identifies the C1-C2 contact and O1-H and O2-H contacts as relevant descriptors associated with bond formation and proton transfer.
Source: Aldol reaction · p. 8The preceding HLDA approach is limited to linearly separable states and requires selecting a small set of uncorrelated descriptors using system knowledge and physical intuition.
Source: p. 2
Abstract
from arXiv · showhide
Designing an appropriate set of collective variables is crucial to the success of several enhanced sampling methods. Here we focus on how to obtain such variables from information limited to the metastable states. We characterize these states by a large set of descriptors and employ neural networks to compress this information in a lower-dimensional space, using Fisher's linear discriminant as an objective function to maximize the discriminative power of the network. We test this method on alanine dipeptide, using the non-linearly separable dataset composed by atomic distances. We then study an intermolecular aldol reaction characterized by a concerted mechanism. The resulting variables are able to promote sampling by drawing non-linear paths in the physical space connecting the fluctuations between metastable basins. Lastly, we interpret the behavior of the neural network by studying its relation to the physical variables. Through the identification of its most relevant features, we are able to gain chemical insight into the process.
Alanine dipeptide
Deep-LDA compresses information from metastable states into nonlinear collective variables that promote transitions between basins. Tests on alanine dipeptide and the aldol reaction show that these variables can follow low-free-energy paths, while feature rankings reveal relevant physical descriptors.
Alanine dipeptide
- Alanine dipeptide descriptors were the 45 heavy-atom distances, a deliberately challenging nonlinearly separable input set that Deep-LDA could handle, and the approach showed robustness across network settings and sampling algorithms.The trained PyTorch model was made usable with enhanced-sampling methods through a PLUMED2 interface [30].Source: Alanine dipeptide · pp. 5–6
- Biasing the Deep-LDA CV produced highly diffusive alanine sampling comparable to biasing φ and ψ, rapidly converged the basin free-energy difference, and reproduced the slow dihedrals.The reported comparisons use the Ramachandran-angle-biased simulations as reference.Source: Alanine dipeptide · pp. 5–6, Figure 2 · p. 5
- For alanine dipeptide, Deep-LDA isolines were learned from basin-only data, and enhanced fluctuations drove the system in a direction correlated with the low-free-energy path between basins.The isolines in intermediate regions are extrapolated by the network.Source: Alanine dipeptide · p. 6, Figure 3 · p. 6
Aldol reaction
- In the aldol reaction, feature ranking identified C1-C2, O1-H, and O2-H contacts as the three leading descriptors, revealing bond formation and proton transfer without prior pathway information.The ranking methods based on first-layer weights and averaged CV derivatives gave similar results.Source: Figure 4 · p. 7, Aldol reaction · p. 8
- For the aldol reaction, Deep-LDA isolines resembled the free-energy contours, and the driven direction followed the minimum-free-energy path, making the CV committor-like.The two basins were clearly separated in the free-energy surface projected onto C1-C2 and O1-H.Source: Figure 4 · p. 7, Aldol reaction · p. 8
- The method learns CVs by nonlinear neural-network dimensionality reduction followed by a linear transformation that maximizes LDA separation; it is intended to promote transitions from limited basin data, not necessarily trace an ideal path.The authors expect it to work best for adjacent basins; intermediate states may be added iteratively, and feature rankings can identify or filter descriptors.Source: Aldol reaction · p. 8
SUPPORTING INFORMATION
The supporting information documents Deep-LDA training and implementation and tests its sampling and free-energy reconstruction on alanine dipeptide and the aldol reaction. It also reports feature analyses and data availability.
SI-1 Neural network training
- Training regularizes the within-class scatter matrix with λ = 0.05 and uses α = 2/λ for robust behavior.The model uses ReLU, 10,000 configurations in batches of 2,000, ADAM with learning rate 10^-4, and L2 weight regularization γ = 10^-5; a custom LibTorch interface loads the model in PLUMED2. Code and inputs are available in PLUMED-NEST as plumID:20.004, and results are archived in Materials Cloud as 2020.0035.Source: SI-1 Neural network training · p. 9, SI-2 PLUMED interface with PyTorch · p. 9, SI-5 Data availability · p. 16
SI-3 Alanine dipeptide
- Using scalar distances alone, Deep-LDA drives alanine-dipeptide transitions by combining them nonlinearly, mimicking the effect of the φ and ψ angles.The comparison is against simulations biased directly along the two Ramachandran angles.Source: SI-3 Alanine dipeptide · pp. 9–10
- The reconstructed alanine-dipeptide free-energy error is below 0.5 kBT in the most relevant regions, with standard deviation below 1 kBT throughout regions of interest.These estimates compare 10 OPES simulations against a reference FES obtained by biasing φ and ψ directly.Source: SI-3 Alanine dipeptide · pp. 9, 11
- All tested alanine-dipeptide cases quickly converge in the basin free-energy difference within the 0.5 kBT uncertainty.The tests vary sampling method, neural-network architecture, and regularization; each estimate uses 10 simulations, with the first 2 ns discarded.Source: SI-3 Alanine dipeptide · pp. 12–13
SI-4 Aldol reaction
- The reweighted aldol free-energy profiles are projected onto three chemical distances identified by feature-importance analysis.The simulation used CP2K at the PM6 level and 40 contacts; the Deep-LDA CV was broadened with s′ = s + s^3 for OPES sampling.Source: SI-4 Aldol reaction · p. 14
- A derivative-based feature ranking qualitatively agrees with the original ranking: the same three contacts are most relevant.The alternative ranking sums the CV derivatives with respect to each input, scaled by that descriptor’s standard deviation, across training configurations.Source: SI-4 Aldol reaction · p. 15
- A Deep-LDA CV trained on all aldol-reaction distances drives transitions between basins, though slightly less efficiently than one trained on contacts.The CV is transformed as s′ = s + s^3 before OPES sampling.Source: SI-4 Aldol reaction · p. 16