MORPH

PDE Foundation Models with Arbitrary Data Modality

Mahindra Singh Rautela · Alexander Most · Siddharth Mansingh · Bradley C. Love
Alexander Scheinker · Diane Oyen · Nathan Debardeleben · Earl Lawrence · Ayan Biswas

Los Alamos National Laboratory

arXiv Code BibTeX

Overview

We introduce MORPH, a multimodal foundation model for partial differential equations (PDEs) designed to learn across heterogeneous physics datasets with varying dimensionalities, resolutions, and fields. Its architecture combines component-wise convolutions, field-wise cross-attention, and factorized axial spatiotemporal attention, enabling scalable learning across diverse PDE modalities. We pretrain multiple model variants on a heterogeneous PDE corpus using a next-frame prediction objective and evaluate transfer across a broad set of downstream tasks.

These include forward modeling tasks such as autoregressive rollouts and terminal key-frame prediction, as well as inverse tasks including composite material property estimation, damage detection in aerospace structures, inertial-confinement-fusion parameter estimation, and sparse sea-surface-temperature reconstruction. Across zero-shot evaluation, full-model fine-tuning, and parameter-efficient low-rank adaptation, pretrained MORPH models consistently outperform models trained from scratch.

MORPH improves data efficiency in low-data regimes, exhibits favorable model- and data-scaling behavior, and generalizes strongly to out-of-distribution physical systems. Collectively, these capabilities establish MORPH as a flexible backbone for learning from the heterogeneous and multimodal nature of scientific observations, charting a path toward scalable and data-efficient scientific machine learning.

Architecture

MORPH maps heterogeneous observations to a common representation, reasons over spatial and temporal structure, and decodes the next physical state.

MORPH architecture diagram showing heterogeneous 1D, 2D, and 3D data unified into a common tensor format, processed by convolution and axial-attention modules, then decoded autoregressively.

Capabilities & downstream tasks

MORPH supports efficient autoregressive forecasting and adapts to forward and inverse scientific learning tasks.

Data efficiency

Pretraining lets MORPH outperform standalone models with substantially fewer task-specific trajectories.

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FNS-KF data can exceed the standalone reference.

Autoregressive prediction

MORPH produces stable multi-step forecasts from an initial state on representative shallow-water and forced Navier–Stokes systems.

Terminal key-frame prediction

Predict a system’s terminal state directly from its initial conditions.

Forward modeling

Composite material property estimation

Infer material properties from observed physical responses.

Inverse modeling

Aerospace structural damage detection

Identify damage in aerospace structures from their measured behavior.

Inverse modeling

Inertial-confinement-fusion parameter estimation

Estimate physical parameters governing inertial-confinement-fusion systems.

Inverse modeling

Sparse sea-surface-temperature reconstruction

Reconstruct complete sea-surface-temperature fields from sparse observations.

Inverse modeling

Data universe

Pretraining · 6 datasets

  • MHD-3D
  • DR-2D
  • CFD-1D
  • CFD2D-IC
  • CFD-3D
  • SW-2D

Fine-tuning · 7 datasets

  • DR-1D
  • CFD-2D
  • CFD3D-TURB
  • BE-1D
  • GSDR-2D
  • TGC-3D
  • FNS-KF-2D

Citation

@article{rautela2025morph,
  title   = {MORPH: PDE Foundation Models with Arbitrary Data Modality},
  author  = {Rautela, Mahindra Singh and Most, Alexander and Mansingh, Siddharth and Love, Bradley C and Scheinker, Alexander and Oyen, Diane and Debardeleben, Nathan and Lawrence, Earl and Biswas, Ayan},
  journal = {arXiv preprint arXiv:2509.21670},
  year    = {2025}
}