Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solvers
Authors: Nima Hosseini Dashtbayaz, Hesam Salehipour, Adrian Butscher, Nigel Morris
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate Φ-ROM on five problems: 1D viscous Burgers (Burgers ) and 2D diffusion (Diffusion) equations, both solved by finite-difference solvers, 2D Korteweg De Vries (Kd V) equation from the spectral solver Exponax [26], 2D Navier-Stokes decaying turbulence problem (N-S) with the finite volume-based solver JAX-CFD [27], and the 2D flow over a cylinder (LBM) using the Lattice Boltzmann solver XLB [28]. This diverse set of PDEs and solvers, spanning fundamentally different numerical methods, highlights the robustness and versatility of Φ-ROM. See Appendix D for detailed descriptions of each problem. For each problem, models are trained on Mtr trajectories of Ttr time steps and evaluated on Mte trajectories to assess forecasting and generalization performance. Evaluation is performed by forecasting solutions for unseen initial conditions or parameters in Ute for Ttr (interpolation) and Tte (extrapolation) time steps. Tables 1, 2, 3, and Figures 3, 4, 7-13 show experimental results and comparisons. |
| Researcher Affiliation | Collaboration | Nima Hosseini Dashtbayaz Department of Computer Science University of Western Ontario London, Ontario, Canada EMAIL Hesam Salehipour Autodesk Research Toronto, Ontario, Canada EMAIL Adrian Butscher Autodesk Research Toronto, Ontario, Canada EMAIL Nigel Morris Autodesk Research Toronto, Ontario, Canada EMAIL |
| Pseudocode | Yes | Algorithm 1 Training procedure of Φ-ROM Algorithm 2 Dynamics loss of Φ-ROM |
| Open Source Code | Yes | Furthermore, Φ-ROM learns to recover and forecast the solution fields even when trained or evaluated with sparse and irregular observations of the fields, providing a flexible framework for field reconstruction and data assimilation. We demonstrate the framework s robustness across various PDE solvers and highlight its broad applicability by providing an open-source JAX implementation that is readily extensible to other PDE systems and differentiable solvers, available at https://phi-rom.github.io. |
| Open Datasets | Yes | Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [Yes] Justification: The code for training the proposed model and all the baselines is submitted as supplemental material and will be published. For each experiment, a bash script is included to train and reproduce the experiment. The code for generating all the required datasets is also provided. |
| Dataset Splits | Yes | Table 4: Summary of the datasets used in the experiments. Mtr, Mte, Mval are the number of training, test, and validation trajectories, Ttr and Tte are the number of training and testing time steps, and m is the number of output scalar fields. For each problem, models are trained on Mtr trajectories of Ttr time steps and evaluated on Mte trajectories to assess forecasting and generalization performance. Evaluation is performed by forecasting solutions for unseen initial conditions or parameters in Ute for Ttr (interpolation) and Tte (extrapolation) time steps. |
| Hardware Specification | Yes | We trained our Burgers and Diffusion models on a single 48GB A6000 GPU, and Kd V, N-S, and LBM models, each on four 40GB A100 GPUs. Training wall-clock times are as follows: 20 minutes for Burgers , 5 hours for Diffusion, 38 hours for N-S, 25 hours for Kd V, and 18 hours for LBM. |
| Software Dependencies | No | We implemented Φ-ROM in the JAX ecosystem using Equinox for building neural networks [50], Diffrax for numerical integration [51], and Optax for gradient optimization. As a result, any numerical solver implemented in JAX can be easily used for training Φ-ROM, and the whole training pipeline, along with the solver step, is compiled and run together. In this work, we experimented with JAX-CFD [27], XLB [28], and Exponax [26] as PDE solvers, while other JAX-based solvers can be adopted as well. Furthermore, JAX transformations allow the training pipeline of Φ-ROM to support multiple GPUs regardless of the implementation of the PDE solver. |
| Experiment Setup | Yes | We choose Adam W [48] optimizer to train Φ-ROM and apply exponential learning rate decay with a decay rate of 0.985 every 50 epochs. (See Appendix F.3 for complete hyperparameters.) Table 5: Network configuration for each problem. Table 6: Training hyperparameters for each problem. |