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AutoPDEBench: Benchmarking LLM Auto-Research for Neural PDE Solver Design

Ruoyan Li, Wei Wang, Yizhou Sun

arXiv:2609.32245v1cs.CEcs.AI

TL;DR

Neural PDE solvers can struggle with domain-specific physical constraints, and designing specialized architectures manually is time-consuming and expertise-intensive. AutoPDEBench evaluates LLM-driven automated research across 25 challenging datasets using general-purpose solver baselines and a multi-agent research pipeline. The agentic system outperforms the general-purpose baselines, though it falls short on some highly complex tasks.

  • Problem

    Existing neural solvers struggle with domain-specific physical challenges, while manually designing specialized architectures requires substantial expertise and time.

    Source: §1 · pp. 1–2

  • Method

    AutoPDEBench evaluates LLM-driven automated solver design on 25 challenging datasets, comparing general-purpose neural solvers with a multi-agent iterative research pipeline.

    Source: §1 · p. 2

  • Results

    The automated research agent consistently outperforms versatile general-purpose baselines across the benchmark.

    Source: §5 · p. 9

  • Takeaways & Limitations

    AutoPDEBench provides an open-ended testbed for agents to pursue increasingly accurate solvers for complex physical systems.

    Source: §1 · p. 2

    The agent fails to surpass general-purpose baselines on highly complex LagFSI and 5,000-step LongHorizon tasks; the authors hypothesize this reflects reliance on pretrained knowledge for novel problems.

    Source: §4 · pp. 6–7

Abstract

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Partial differential equations (PDEs) are essential for modeling complex physical systems, and neural solvers have recently emerged as powerful data-driven tools for numerically solving them. However, existing neural solvers struggle with domain-specific challenges, such as varying parameters and high-speed flows, necessitating specialized architectures. Manually designing these specialized solver architectures is a highly iterative, time-consuming process requiring deep expertise, creating a significant bottleneck in scientific discovery. We propose leveraging autonomous AI research agents to automate the synthesis of specialized solvers. To support this, we introduce AutoPDEBench, a benchmark dedicated to LLM-driven automated research for PDE solver design. The benchmark includes 25 challenging datasets featuring both novel and actively studied physical scenarios. We evaluate a suite of general-purpose models (transformer, ROM, and graph-based) alongside a multi-agent instantiation of the iterative automated research pipeline, which serves as an agentic baseline. Empirical results show that the iterative automated research system significantly outperforms the general-purpose neural solver baselines. Our findings demonstrate the viability of using AI agents to automatically design neural solvers for complex physical systems. AutoPDEBench provides a foundational testbed to accelerate agent-driven scientific discovery in physics and engineering.

1 INTRODUCTION

Neural PDE solvers face physical settings that require specialized mechanisms, while manually designing those solvers demands substantial expertise and time. AutoPDEBench evaluates LLM-driven solver design across 25 challenging datasets, and its agentic baseline outperforms general-purpose neural solver baselines.

1 INTRODUCTION

  • Varying PDE parameters can make standard solvers unable to map initial conditions reliably, while high-speed flows challenge stability and physical fidelity.Prior approaches addressed these settings with parameter-guided channel attention and adaptive timestep prediction, respectively.Source: §1 · p. 1
  • Manual design of domain-specific solvers requires deep expertise, substantial time, and computational resources, limiting the pace and scalability of scientific discovery.The process is highly iterative and tailored to each physical system.Source: §1 · p. 1
  • AutoPDEBench comprises 25 challenging datasets spanning actively studied and entirely novel physical scenarios with distinct constraints.The benchmark is intended for LLM-driven automated research on specialized solver design.Source: §1 · p. 2
  • The iterative automated research system outperforms versatile, general-purpose neural solver baselines on the benchmark.The evaluation compares general-purpose solvers with a multi-agent instantiation of the research pipeline.Source: §1 · p. 2

2 RELATED WORK

Prior work has expanded neural PDE solvers across representations, physical settings, and applications, while LLM-based neural-solver design has so far been evaluated on standard benchmarks. AutoPDEBench targets complex physical constraints and novel systems with an automated research-agent approach.

Neural PDE Solvers

  • Neural PDE solver research spans grid, mesh, and particle representations, with later work addressing varied PDE parameters, boundary conditions, geometries, dimensions, and physical representations.Benchmark suites and physics foundation models are also part of this trajectory.Source: §2 · p. 3
  • Neural methods also address inverse problems and hybrid frameworks that incorporate networks into classical numerical schemes.The cited hybrid work aims to enhance scheme performance and mitigate truncation errors.Source: §2 · p. 3

LLM for PDE Solvers

  • Prior LLM-agent studies of neural solver design evaluated on standard benchmarks, whereas this work targets complex datasets requiring domain-specific solvers.Its novel, previously unstudied systems require agents to identify physical bottlenecks and synthesize architectural solutions rather than retrieve memorized templates.Source: §2 · p. 3

LLM Auto Research

  • LLM research has progressed from localized assistance toward more autonomous agents and end-to-end scientific discovery pipelines.The progression includes literature review, idea generation, experimental planning, machine-learning modeling, and governing-equation identification.Source: §2 · pp. 3–4

3 AUTOPDEBENCH

AutoPDEBench specifies a shared evaluation setting for neural simulators and automated research agents, then provides datasets, evaluation protocols, general-purpose baselines, and a reference multi-agent pipeline. Its benchmark covers diverse physical constraints and representations under a fixed GPU memory budget.

3.1 PROBLEM FORMULATION

  • The agentic system maps available context into a model, training objective, and hyperparameters over repeated rounds, selecting the best validation-performing candidate under a GPU memory limit.It observes validation outcomes, not test-set quantities, and reports performance on the held-out test split.Source: §3.1 · pp. 4–5

3.2 DATASETS

  • The benchmark contains 25 datasets with unique constraints, including novel and understudied physical systems.Table 1 provides an overview; detailed generation, physics, and problem setups are described in dataset-specific appendices.Source: §3.2 · p. 5, Table 1 · p. 5

3.3 EVALUATION PROTOCOL

  • Final performance is evaluated on the test dataset, primarily with RMSE and with dataset-specific metrics for additional physical or practical properties.Models are tuned within GPU resource constraints.Source: §3.3 · p. 5

3.4 GENERAL-PURPOSE NEURAL SOLVER BASELINES

  • The general-purpose baselines include transformer-, ROM-, and graph-based methods selected to handle unstructured and dimensionally diverse inputs.The study identifies GNOT, Transolver, Transolver++, LNO, and AMG as representative baselines; current foundation models are excluded because their grid-oriented representations and rigid mappings do not fit the benchmark's inputs.Source: §3.4 · p. 6

3.5 MULTI-AGENT INSTANTIATION OF AUTO RESEARCH PIPELINE

  • The reference auto-research system uses a planner, coder, and debugger to plan solver designs, produce executable files, and revise failed runs.Debugging is invoked for execution errors or memory-budget violations and repeats until success or the retry budget is exhausted.Source: §3.5 · p. 6

4 EXPERIMENTS

The experiments compare the agentic solver with general-purpose and domain-specific models, examine backbone sensitivity and cross-PDE transfer, and extend optimization to 30 iterations. The agent significantly outperforms general-purpose neural solvers overall, while performance varies by backbone, task, and optimization horizon.

4 EXPERIMENTS

  • The multi-agent system significantly outperforms general-purpose neural solvers overall, using RMSE as the primary metric.Table 2 compares general-purpose neural solvers with agent-designed models using gpt-5.5 as the backbone.Source: §4 · p. 6, Table 2 · p. 7

4.1 LLM BACKBONE SENSITIVITY ANALYSIS

  • Flagship backbones perform strongly across three representative tasks, but general LLM leaderboard performance does not reliably predict these physical-task results.gpt-5.5, gpt-5.6-sol, fable-5, opus-4.8, and grok-4.5 perform strongly; gpt-5.6-sol underperforms or matches gpt-5.5 across the three cases.Source: §4.1 · pp. 7–8

4.2 COMPARISON WITH DOMAIN-SPECIFIC BASELINES

  • The agent’s designs outperform NeuralCFL, CAPE, and UPT across the evaluated HighSpeedFlow, MixedParam, and LagInletOutlet domains.The comparisons use dataset-specific human-designed baselines; Figure 4 presents the results.Source: §4.2 · p. 8, Figure 4 · p. 9

4.3 TRANSFERABILITY ACROSS PDES

  • Agent-designed architectures transfer successfully to different physical scenarios that share similar dataset-specific challenges.The tested settings include coal-dust explosion, variable-viscosity 2D Burgers’ equation, and a 2D wave dataset.Source: §4.3 · pp. 8–9, Figure 5 · p. 9

4.4 AGENT LONG-HORIZON SCALABILITY

  • Across 30 optimization iterations, the agent improves designs for HighSpeedFlow and MixedParam but struggles on LagInletOutlet.MixedParam improves significantly after iteration 10; the agent makes conservative hyperparameter adjustments and minor tweaks on the other two tasks.Source: §4.4 · p. 9, Figure 6 · p. 9

5 CONCLUSION

The paper concludes that AutoPDEBench provides a platform for evaluating LLM-driven automated research in neural PDE solvers. It frames PDE-focused agent evaluation as relevant to complex physical applications and future scientific discovery.

5 CONCLUSION

  • AutoPDEBench brings together 25 challenging datasets to evaluate LLM-driven automated research for neural PDE solvers.The benchmark includes complex physical constraints and scenarios that are actively studied or novel.Source: §5 · p. 9

A BROADER IMPACT

  • The benchmark grounds agent evaluation in PDE challenges relevant to climate forecasting, aerospace engineering, fluid dynamics, and materials science.The authors hope the platform will help pave the way for autonomous research that accelerates scientific discovery across disciplines.Source: A BROADER IMPACT · p. 17

B LIMITATION AND FUTURE WORK

The authors note that the benchmark has relatively few samples compared with other LLM benchmarks and intend to expand it as new challenges emerge.

B LIMITATION AND FUTURE WORK

  • The benchmark has relatively few samples compared with other LLM benchmarks, but its datasets are curated around specialized, recent physical challenges.The authors state that LLMs have no prior exposure to the solutions in their training corpora.Source: B LIMITATION AND FUTURE WORK · p. 17
  • The authors plan to add datasets over time and invite researchers to contribute complex physical challenges.They aim to collaborate across more disciplines and include systems with constraints that challenge existing general-purpose solvers.Source: B LIMITATION AND FUTURE WORK · p. 17

C EVALUATION METRICS

The evaluation metrics compare predicted states with ground truth across grid, mesh, and particle representations. They pair general state error with measures of spectral structure, physical quantities, boundary behavior, and particle-state utility.

C EVALUATION METRICS

  • RMSE measures pointwise discrepancy across samples, channels, and spatial locations, with its summation domain following the state representation.The metric covers Eulerian grids, Eulerian meshes, and Lagrangian particles.Source: C EVALUATION METRICS · p. 17
  • FRMSE compares Eulerian-grid amplitude spectra, exposing differences in spatial-frequency content that pointwise RMSE may miss.It can reveal smeared fine features or spurious high-frequency noise despite similar pointwise error.Source: C EVALUATION METRICS · p. 18
  • Kinetic and magnetic energy errors measure absolute errors in their respective energy densities, exposing over- or under-energetic flows and magnetic-energy discrepancies.These physical quantities can reveal discrepancies not singled out by pointwise state error.Source: C EVALUATION METRICS · p. 18
  • MassE evaluates RMSE of total mass for the advection equation, directly probing deviation from mass conservation.The total mass is the discrete spatial integral of the state, reduced over samples and channels.Source: C EVALUATION METRICS · p. 18
  • BoundaryRMSE restricts RMSE to the domain’s outer frame to assess boundary-condition enforcement that whole-domain averages can dilute.The boundary may contain only a small fraction of the nodes.Source: C EVALUATION METRICS · p. 18
  • LagKE computes particle kinetic energy with unit masses and measures RMSE of that scalar across the split.Because velocities are finite-differenced from predicted positions, the metric is sensitive to temporal inconsistency.Source: C EVALUATION METRICS · pp. 18–19
  • EuARMSE and EuAFRMSE interpolate particle velocities onto grid nodes with an SPH kernel before applying grid metrics, approximating downstream fixed-location queries.The resulting metrics assess the practical utility of predicted particle trajectories.Source: C EVALUATION METRICS · p. 19
  • Sinkhorn compares particle position sets as unordered distributions, while Coeff measures RMSE of a derived physical coefficient against its reference value.Sinkhorn avoids requiring particlewise correspondence; Coeff tests accuracy of an engineering-relevant scalar.Source: C EVALUATION METRICS · p. 19

D HARDWARE SPECIFICATIONS

Experiments were run on servers or workstations with several CPU, memory, and GPU configurations.

D HARDWARE SPECIFICATIONS

E SUPPLEMENTARY EXPERIMENTS ON TRANSFERABILITY ACROSS PDES

The supplementary transfer experiments apply agent-designed solver architectures to three different PDE settings. The reported designs retain superior accuracy or optimal performance in these new environments.

E SUPPLEMENTARY EXPERIMENTS ON TRANSFERABILITY ACROSS PDES

F SUPPLEMENTARY EXPERIMENTS ON LLM BACKBONE ANALYSIS

The supplementary backbone-sensitivity analysis evaluates alternative LLMs on three datasets. Its tables report RMSE and additional metrics, but the supplied passages do not state comparative outcomes.

F SUPPLEMENTARY EXPERIMENTS ON LLM BACKBONE ANALYSIS

G SUPPLEMENTARY EXPERIMENT ON AGENT LONG-HORIZON SCALABILITY

The long-horizon scalability experiments report that supplementary metrics generally track RMSE, suggesting successive agent iterations improve both point-wise error and physical consistency.

G SUPPLEMENTARY EXPERIMENT ON AGENT LONG-HORIZON SCALABILITY

  • Supplementary metrics generally align with RMSE, indicating that successive agent designs improve both point-wise error and physical consistency.The reported supplementary results cover validation and test data for HighSpeedFlow, MixedParam, and LagInletOutlet.Source: G SUPPLEMENTARY EXPERIMENT ON AGENT… · p. 22
  • Tables 9–14 report supplementary metrics for agent iterations extending to 30 steps across HighSpeedFlow, MixedParam, and LagInletOutlet.Tables 9, 11, and 13 report validation results; Tables 10, 12, and 14 report test results.Source: Table 9 · p. 22, Table 10 · p. 22, Table 11 · p. 23

H DATASET TAXONOMY

AutoPDEBench organizes its datasets by five challenge categories, allowing datasets to belong to multiple categories and grouping them in a taxonomy table.

H DATASET TAXONOMY

  • AutoPDEBench groups dataset challenges into generalization, domains and forcing, complex physics, scale, and observational irregularity.The categories cover variation across problem instances, complex dynamics, computational demands, and imperfect observations.Source: H DATASET TAXONOMY · p. 25
  • Datasets may span multiple categories; Table 15 assigns them in a block-diagonal layout, placing cross-category datasets at the boundaries between blocks.The table summarizes the category assignment for each dataset.Source: H DATASET TAXONOMY · p. 25, Table 15 · p. 25

I DATASETS

The dataset appendix provides detailed descriptions while keeping mathematical notation local to each section; datasets come from literature or validated numerical simulations.

I DATASETS

  • The appendix provides a comprehensive breakdown of each dataset introduced in the study.A single global mathematical glossary is impractical, so symbols are defined within their respective sections and may denote different quantities elsewhere.Source: I DATASETS · p. 26
  • Datasets are adapted from peer-reviewed literature or simulated with established schemes, and simulated solvers are checked against analytical solutions and spatial and temporal convergence studies.The stated validation checks verify that simulation results are grid-independent.Source: I DATASETS · p. 26

I.1 HIGHSPEEDFLOW

The four dataset sections describe distinct modeling challenges, from shocks and noisy measurements to parameter variation and heterogeneous particle dynamics. Where results are reported, the automated research agent outperforms general-purpose baselines.

I.1 HIGHSPEEDFLOW

  • HighSpeedFlow models a compressible circular blast with shocks and turbulent instabilities, while adaptive resolution produces non-uniform time steps.The modeling objective is to map temperature, density, and velocity fields at an input time to a requested target time.Source: §I.1 · p. 26
  • The automated research agent significantly outperforms general-purpose baseline solvers on HighSpeedFlow across RMSE, FRMSE, and Kinetic Energy.The evaluation uses an Eulerian grid; Table 16 presents the complete results.Source: §I.1 · p. 27, Table 16 · p. 27

I.2 REALDATA

  • RealData uses measured two-dimensional cylinder-flow velocities, where sensor noise can obscure dynamics and challenge temporal stability.PIV estimates in-plane velocity from tracer displacement; noise and finite sampling mean the data satisfy Navier–Stokes only approximately.Source: §I.2 · p. 29
  • The automated research agent yields substantial improvements over standard solvers on RealData across RMSE, FRMSE, and Kinetic Energy.The evaluation uses an Eulerian grid; Table 17 presents the comprehensive results.Source: §I.2 · p. 30, Table 17 · p. 30

I.3 MIXEDPARAM

  • MixedParam varies Reynolds number across trajectories, requiring parameter-conditioned modeling and zero-shot generalization to intermediate test values.Training samples Reynolds numbers at intervals of 100, while validation and test use intervals of 25.Source: §I.3 · p. 31
  • The automated research agent achieves significantly higher accuracy than standard baselines on MixedParam across RMSE, FRMSE, and Kinetic Energy.Table 18 presents the complete experimental results on the Eulerian-grid dataset.Source: §I.3 · p. 32, Table 18 · p. 32

I.4 HETEROGENEOUS

  • Heterogeneous Rayleigh–Taylor trajectories vary in density contrast, so one simulator must capture attribute-conditional dynamics from smooth flows to chaotic mixing.Simply concatenating the physical attribute into node features may not adequately condition the learned dynamics.Source: §I.4 · p. 33

I.5 PARTIAL

The Partial dataset tests forecasting from incomplete observations, while MixedDomain tests whether one solver can forecast the same flow across grid, mesh, and particle representations. The agent’s specialized design outperforms general-purpose baselines on Partial, whereas MixedDomain centers on reconciling structurally different representations of identical dynamics.

I.5 PARTIAL

  • Partial forecasting maps masked current observations to the complete future vorticity field, with randomly generated masks applied after trajectory generation.The underlying flow is incompressible Navier–Stokes at Re = 1000.Source: §I.5 · p. 36
  • Partial observability makes forecasting ill-posed because hidden spatial information leaves multiple full states consistent with one masked observation.The model must infer unobserved regions while predicting temporal evolution.Source: §I.5 · p. 36
  • On Partial, the automated agent’s architecture surpasses general-purpose baselines on RMSE, FRMSE, and Kinetic Energy.Table 20 reports the complete Eulerian-grid comparison.Source: §I.5 · p. 36, Table 20 · p. 36

I.6 MIXEDDOMAIN

  • MixedDomain’s unified simulator accepts any of the three representations and predicts the next-step velocity field in that same representation.Its input includes node positions, five-step velocity history, and a representation identifier.Source: §I.6 · p. 38
  • MixedDomain requires one solver to handle grid, mesh, and particle data with different node counts, connectivity, and geometric structure despite their shared physics.The challenge includes learning consistent dynamics across disparate sampling densities without fixed topology.Source: §I.6 · p. 38
  • The grid and mesh versions are interpolated from a native Lagrangian SPH simulation, so all three representations derive from one underlying flow.The Eulerian versions use SPH kernel interpolation.Source: §I.6 · p. 38

I.7 MULTIPHYSICS

This section covers coupled multiphysics, irregular-time fluid prediction, and Lagrangian particle simulations. It reports agent performance across these settings, including errors and practical-utility measures on LagFSI.

I.7 MULTIPHYSICS

  • The agent’s design achieves substantially better performance on 3D MHD turbulence; AMG is unsuitable because its graph architecture scales poorly to large 3D datasets.Performance is evaluated with RMSE, FRMSE, Kinetic Energy, and Magnetic Energy. The dataset represents a 7-channel state on a 64 × 64 × 64 grid, where each snapshot contains over 1.8 million data points.Source: §I.8 · pp. 44–45, Table 23 · p. 45

I.9 IRREGULARTIME

  • The agent’s design consistently achieves superior performance across all evaluated metrics on the IrregularTime dataset.The model must condition on a continuous time increment dt and remain accurate across gaps that require either accumulated nonlinear evolution or near-identity behavior.Source: Table 24 · p. 47, §I.9 · p. 47

I.10 LAGINLETOUTLET

  • LagInletOutlet removes one-to-one particle correspondence, requiring the model to represent a continuous flow field and predict velocity at query positions decoupled from the input particles.The open-domain jet continuously injects particles at the inlet and removes them at the outlets, so particle identity and count change between steps.Source: §I.10 · p. 49

I.11 LAGFSI

  • LagFSI requires one model to capture coupled fluid and rigid-body dynamics while maintaining mutually consistent solid-particle motion during rollout.Rigidity is not explicitly enforced in the predicted velocities, so small inconsistencies can accumulate into sphere stretching, shearing, or fragmentation; the model predicts next-step particle velocities using particle features and type labels.Source: §I.11 · p. 51
  • The agent performs poorly across all evaluated metrics; Table 26 reports fluid/solid error components, domain-averaged RMSE, physical consistency, and practical utility.The RMSE in the main table averages across the fluid and solid domains.Source: §I.11 · p. 52, Table 26 · p. 53

I.12 EXTREME

This section presents diverse challenging PDE benchmarks spanning extreme dynamics, changing conditions, forcing, particle simulations, high-dimensional states, and irregular 3D geometry. It examines agent-designed architectures across these settings, including simulation-to-real generalization and long-horizon evaluation.

I.12 EXTREME

  • The proposed design outperforms the compared models on Extreme; GNOT training diverges and AMG is omitted because its 3D training cost is infeasible.The dataset’s sharply localized, heavy-tailed fields span extreme value ranges, making naive normalization ineffective and destabilizing training and rollouts.Source: §I.12 · pp. 54–55, Table 27 · p. 55

I.13 MIXEDRES

  • The agent consistently achieves superior performance on MixedRes; AMG is computationally infeasible on 512×512 data, taking 28,000 seconds per epoch.The model must use positional coordinates to infer physical grid spacing across domains and handle a 256× range in grid-point counts.Source: Table 28 · p. 56, §I.13 · p. 56

I.14 EXTLAG1

  • The agent achieves strong results across all evaluated ExtLag1 metrics, including particle-distribution and Eulerian aggregated measures.The global sloshing excitation is shared across particles, so conditioning must inject it effectively rather than merely concatenate it to each particle’s features.Source: §I.14 · pp. 58–59, Table 29 · p. 59

I.15 EXTLAG2

  • ExtLag2 tests whether a solver can propagate piston-driven forcing from boundary particles through the fluid bulk.The prescribed piston velocity is supplied as a known driver, and the loss is evaluated only on fluid particles.Source: §I.15 · p. 60

I.16 MIXEDDIM

  • The proposed design achieves superior performance on MixedDim across 1D, 2D, and 3D, while AMG is impractical because of its poor scaling to 3D.A single model must generalize across all dimensions despite inputs ranging from 64 to 262,144 nodes.Source: §I.16 · p. 62, Table 31 · p. 63

I.17 MIXEDBC

  • MixedBC tests one advection equation across Dirichlet, Neumann, and periodic boundaries, requiring a model to interpret boundary values conditionally by boundary type.The same input slot represents state values, fluxes, or uninformative padding depending on the boundary type.Source: §I.17 · p. 64

I.18 LONGHORIZON

  • The agent exhibits significantly worse performance on the LongHorizon dataset, whose 5000-step autoregressive evaluation makes temporal stability critical.Even small biases or high-frequency artifacts can accumulate into unbounded growth or artificial damping over the rollout.Source: §I.18 · p. 67, Table 33 · p. 67

I.19 STOCHASTIC

  • Stochastic evaluates 20-step predictions for a 2D Φ4 equation, requiring the model to use the full realized noise path rather than only the current state.The noise path is supplied as 20 input channels, and the dataset includes both renormalized and plain explicit trajectories.Source: §I.19 · p. 69

I.20 MULTIPHASE

  • MultiPhase tests whether a single particle model can capture liquid–gas behavior and interface coupling while preventing unphysical mixing during long rollouts.Liquid and gas have contrasting physical properties, and the interface deforms under sloshing.Source: §I.20 · p. 71

I.21 MIXEDPDE

  • MixedPDE combines four systems with distinct physics and channel counts, requiring PDE-conditioned dynamics and support for variable input and output dimensions.The systems are advection-diffusion, Burgers, Gray-Scott, and Navier-Stokes in vorticity form.Source: §I.21 · p. 73

I.22 LARGELAG

  • LargeLag contains two-dimensional Lagrangian simulations of flow around a cylinder, with more than 2 million fluid and solid particles per frame and an open domain.Particles enter at the inlet and leave at the outlet.Source: §I.22 · p. 75
  • LargeLag’s particle scale makes memory the dominant constraint, ruling out methods whose costs grow quadratically with particle count.Dense global attention and dense neighborhood graphs are infeasible for this large-scale particle set.Source: §I.22 · p. 75

I.23 SIM2REAL

  • The agent-proposed architecture exhibits poor performance on Sim2Real, where it must generalize from simulated flow to noisy real-world measurements.The dataset couples an elastically mounted cylinder and fluid through vortex-induced vibration, so accurate, temporally stable rollouts must capture dynamics rather than simulation-specific artifacts.Source: §I.23 · p. 77, Table 38 · p. 78

I.24 HIGHDIMENSIONAL

  • HighDimensional evaluation uses RMSE alone and has no general-purpose baselines, as the state spans five heterogeneous phase-space axes with roughly 22.3 million degrees of freedom.Each float32 state occupies roughly 85 MB, requiring small batches and memory-efficient architectures; conventional spatial convolutions, pixel-wise attention, and spatial FFT layers do not transfer directly.Source: §I.24 · pp. 79–80, Table 39 · p. 80

I.25 COMPLEXGEOMETRY

  • The agent-proposed architecture exhibits sub-optimal performance on ComplexGeometry, which evaluates volumetric, surface, and drag-coefficient RMSE.The task predicts velocity and pressure on an unstructured point cloud spanning car surfaces and surrounding volume at different densities; geometry changes shape separated flow, wake, and surface pressure.Source: §I.25 · pp. 82–83, Table 40 · p. 83

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