PDE Foundation Models

PDE: Partial Differential Equation

Latest papers

11 papers2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Beyond Local Accuracy: Benchmarking the Rollout Reliability of PDE Foundation Models
Oct 22, 2026Jaewan Park, Seid Koric, Giri Krishnan +2PDE Foundation Models PDE Surrogate Modeling
National Center for Supercomputing Applications (NCSA), University of Illinois Urbana–Champaign · Georgia Institute of Technology
FoundPDE: A generative foundation model for data-driven symbolic discovery of partial differential equations
Oct 18, 2026Langchen Liu, Junlin Luo, Min Zhu +2PDE Discovery PDE Foundation Models
Department of Statistics and Data Science, Yale University, New Haven, CT 06511, USA · Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA · Department of Chemical and Environmental Engineering, Yale University, New Haven, CT 06511, USA
Distillation of Foundation Models for Time-dependent PDEs
Aug 12, 2026Daniel Musekamp, Boshra Ariguib, Andrei Manolache +1Efficient Neural Network Inference PDE Surrogate Modeling
University of Stuttgart · University of Cologne · Bitdefender
Unsupervised Adaptation of PDE Foundation Models
Aug 7, 2026Ziye Song, Zhao Wei, Xin Yu +2Unsupervised Domain Adaptation Low-Rank Adaptation
Nanyang Technological University · CFAR, A*STAR · Adelaide University
ARC-STAR: Auditable Post-Hoc Correction for PDE Foundation Models
May 21, 2026Chengze Li, Lingwei Wei, Li Sun +7PDE Surrogate Modeling PDE Foundation Models
University of Illinois Chicago · 2Beijing University of Posts and Telecommunications · 3North China Electric Power University
Tadpole: Autoencoders as Foundation Models for 3D PDEs with Online Learning
May 14, 2026Qiang Liu, Felix Koehler, Benjamin Holzschuh +13D Foundation Models PDE Surrogate Modeling
TUM School of Computation, Information and Technology, Technical University of Munich, Garching, Germany · MCML, Munich Center for Machine Learning, Munich, Germany
jNO: A JAX Library for Neural Operator and Foundation Model Training
May 11, 2026Leon Armbruster, Rathan Ramesh, Georg Kruse +1PDE Foundation Models PDE Operator Learning
Fraunhofer Institute for Integrated Systems and Device Technology IISB, Germany
Physics-informed fine-tuning of foundation models for partial differential equations
Mar 16, 2026Vlad Medvedev, Leon Armbruster, Christopher Straub +2PDE Foundation Models PDE Surrogate Modeling
Department Modeling and Artificial Intelligence Fraunhofer Institute for Integrated Systems and Device Technology IISB Schottkystrasse 10, 91058 Erlangen, Germany
PDE foundation model-accelerated inverse estimation of system parameters in inertial confinement fusion
Mar 4, 2026Mahindra Rautela, Alexander Scheinker, Bradley Love +4PDE Foundation Models Parameter Estimation
AOT-IC Group, Los Alamos National Laboratory, Los Alamos, NM, USA · CAI Division, Los Alamos National Laboratory, Los Alamos, NM, USA · HPC Division, Los Alamos National Laboratory, Los Alamos, NM, USA
Out-of-distribution transfer of PDE foundation models to material dynamics under extreme loading
Mar 4, 2026Mahindra Rautela, Alexander Most, Siddharth Mansingh +9PDE Foundation Models OOD Generalization
AOT-IC Group, Los Alamos National Laboratory, Los Alamos, New Mexico, US, 87545 · CAI Division, Los Alamos National Laboratory, Los Alamos, New Mexico, US, 87545 · EES Divison, Los Alamos National Laboratory, Los Alamos, New Mexico, US, 87545 +2
PDE foundation models are skillful AI weather emulators for the Martian atmosphere
Feb 16, 2026Johannes Schmude, Sujit Roy, Liping Wang +10PDE Foundation Models Weather Forecasting
IBM Research · NASA Marshall Space Flight Center, Huntsville, Al, USA · Earth System Science Center, University of Alabama in Huntsville, Al, USA +1

Oct 22, 2026J/K move · Enter open · S save

Beyond Local Accuracy: Benchmarking the Rollout Reliability of PDE Foundation Models

Jaewan Park, Seid Koric, Giri Krishnan, Sudhakar Pamidighantam+1

National Center for Supercomputing Applications (NCSA), University of Illinois Urbana–Champaign · Georgia Institute of Technology

PDE Foundation Models PDE Surrogate Modeling Forecasting Benchmarks

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PDE foundation models enable data-efficient adaptation but are deployed autoregressively, so short-horizon accuracy need not imply reliable simulation. We ask whether the short-horizon advantage of a foundation-model recipe persists when its predictions are repeatedly fed back as inputs for a long horizon. We define error amplification as G=E(H_f)/E(H_s), which measures full-horizon error relative to short-horizon error. We evaluate seven models on seven two-dimensional time-dependent PDE datasets: scratch-trained FNO and DeepONet; fine-tuned DPOT, GPhyT, Poseidon, and Walrus; and frozen in-context VICON. We report VRMSE, relative L_2, and relative MAE. Six datasets provide paired short- and full-horizon scores, while CE-RM contributes short-rollout sweeps only. At least one fine-tuned foundation model outperforms both scratch baselines in 26 of 30 short-rollout dataset--budget cells under every metric. Nevertheless, full-horizon VRMSE exceeds short-horizon VRMSE in 140 of 144 paired trained configurations, with a median error amplification of

2.04

. The count below VRMSE one falls from 104 to 53, and 12 full rollouts exceed ten although none does at the short horizon. Walrus achieves the lowest full-horizon VRMSE in 16 of 24 cells, yet its median error amplification is

2.70

. Relative L_2 and relative MAE show the same qualitative pattern. These results show that favorable short-horizon rankings can coexist with substantial error amplification. PDE foundation-model benchmarks should therefore report horizon-resolved absolute errors, amplification statistics, and failure incidence rather than a single local forecast score.