MORPH: Shape-agnostic PDE Foundation Models

• URL: http://arxiv.org/abs/2509.21670v2
• Date: Wed, 08 Oct 2025 19:06:50 GMT
• Title: MORPH: Shape-agnostic PDE Foundation Models
• Authors: Mahindra Singh Rautela, Alexander Most, Siddharth Mansingh, Bradley C. Love, Ayan Biswas, Diane Oyen, Earl Lawrence,
• Abstract summary: MORPH is a shape-agnostic, autoregressive foundation model for partial differential equations (PDEs)<n>It is built on a convolutional vision backbone that seamlessly handles heterogeneous evaluations of varying data dimensionality (1D--3D)<n>Across extensive datasets, MORPH matches or surpasses strong baselines and recent state-of-the-art models.
• Score: 37.26306668589026
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce MORPH, a shape-agnostic, autoregressive foundation model for partial differential equations (PDEs). MORPH is built on a convolutional vision transformer backbone that seamlessly handles heterogeneous spatiotemporal datasets of varying data dimensionality (1D--3D) at different resolutions, multiple fields with mixed scalar and vector components. The architecture combines (i) component-wise convolution, which jointly processes scalar and vector channels to capture local interactions, (ii) inter-field cross-attention, which models and selectively propagates information between different physical fields, (iii) axial attentions, which factorizes full spatiotemporal self-attention along individual spatial and temporal axes to reduce computational burden while retaining expressivity. We pretrain multiple model variants on a diverse collection of heterogeneous PDE datasets and evaluate transfer to a range of downstream prediction tasks. Using both full-model fine-tuning and parameter-efficient low-rank adapters (LoRA), MORPH outperforms models trained from scratch in both zero-shot and full-shot generalization. Across extensive evaluations, MORPH matches or surpasses strong baselines and recent state-of-the-art models. Collectively, these capabilities present a flexible and powerful backbone for learning from heterogeneous and multimodal nature of scientific observations, charting a path toward scalable and data-efficient scientific machine learning. The source code, datasets, and models are publicly available at https://github.com/lanl/MORPH.

Related papers

• Nonparametric Data Attribution for Diffusion Models [57.820618036556084]
  Data attribution for generative models seeks to quantify the influence of individual training examples on model outputs.<n>We propose a nonparametric attribution method that operates entirely on data, measuring influence via patch-level similarity between generated and training images.
  arXiv  Detail & Related papers  (2025-10-16T03:37:16Z)
• Learning Divergence Fields for Shift-Robust Graph Representations [73.11818515795761]
  In this work, we propose a geometric diffusion model with learnable divergence fields for the challenging problem with interdependent data. We derive a new learning objective through causal inference, which can guide the model to learn generalizable patterns of interdependence that are insensitive across domains.
  arXiv  Detail & Related papers  (2024-06-07T14:29:21Z)
• FissionFusion: Fast Geometric Generation and Hierarchical Souping for Medical Image Analysis [0.7751705157998379]
  The scarcity of well-annotated medical datasets requires leveraging transfer learning from broader datasets like ImageNet or pre-trained models like CLIP. Model soups averages multiple fine-tuned models aiming to improve performance on In-Domain (ID) tasks and enhance robustness against Out-of-Distribution (OOD) datasets. We propose a hierarchical merging approach that involves local and global aggregation of models at various levels.
  arXiv  Detail & Related papers  (2024-03-20T06:48:48Z)
• Coupled generator decomposition for fusion of electro- and magnetoencephalography data [1.7102695043811291]
  Data fusion modeling can identify common features across diverse data sources while accounting for source-specific variability. We introduce the concept of a textitcoupled generator decomposition and demonstrate how it generalizes sparse principal component analysis for data fusion.
  arXiv  Detail & Related papers  (2024-03-02T12:09:16Z)
• Synthetic location trajectory generation using categorical diffusion models [50.809683239937584]
  Diffusion models (DPMs) have rapidly evolved to be one of the predominant generative models for the simulation of synthetic data. We propose using DPMs for the generation of synthetic individual location trajectories (ILTs) which are sequences of variables representing physical locations visited by individuals.
  arXiv  Detail & Related papers  (2024-02-19T15:57:39Z)
• VTAE: Variational Transformer Autoencoder with Manifolds Learning [144.0546653941249]
  Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables. The nonlinearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning. We show that geodesics and accurate computation can substantially improve the performance of deep generative models.
  arXiv  Detail & Related papers  (2023-04-03T13:13:19Z)
• Interpretable and Scalable Graphical Models for Complex Spatio-temporal Processes [3.469001874498102]
  thesis focuses on data that has complex-temporal structure and on probabilistic graphical models that learn the structure in an interpretable and interpretable manner. practical applications of the methodology are considered using real datasets. This includes brain-connectivity analysis using data, space weather forecasting using solar imaging data, longitudinal analysis of public opinions using Twitter data, and mining of mental health related issues using TalkLife data.
  arXiv  Detail & Related papers  (2023-01-15T05:39:30Z)
• Scalable Regularised Joint Mixture Models [2.0686407686198263]
  In many applications, data can be heterogeneous in the sense of spanning latent groups with different underlying distributions. We propose an approach for heterogeneous data that allows joint learning of (i) explicit multivariate feature distributions, (ii) high-dimensional regression models and (iii) latent group labels. The approach is demonstrably effective in high dimensions, combining data reduction for computational efficiency with a re-weighting scheme that retains key signals even when the number of features is large.
  arXiv  Detail & Related papers  (2022-05-03T13:38:58Z)
• Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data [50.23363975709122]
  We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
  arXiv  Detail & Related papers  (2022-02-18T22:41:51Z)
• Hierarchical Graph-Convolutional Variational AutoEncoding for Generative Modelling of Human Motion [1.2599533416395767]
  Models of human motion commonly focus either on trajectory prediction or action classification but rarely both. Here we propose a novel architecture based on hierarchical variational autoencoders and deep graph convolutional neural networks for generating a holistic model of action over multiple time-scales. We show this Hierarchical Graph-conational Varivolutional Autoencoder (HG-VAE) to be capable of generating coherent actions, detecting out-of-distribution data, and imputing missing data by gradient ascent on the model's posterior.
  arXiv  Detail & Related papers  (2021-11-24T16:21:07Z)
• Equivariant vector field network for many-body system modeling [65.22203086172019]
  Equivariant Vector Field Network (EVFN) is built on a novel equivariant basis and the associated scalarization and vectorization layers. We evaluate our method on predicting trajectories of simulated Newton mechanics systems with both full and partially observed data.
  arXiv  Detail & Related papers  (2021-10-26T14:26:25Z)
• Dynamical Deep Generative Latent Modeling of 3D Skeletal Motion [15.359134407309726]
  Our model decomposes highly correlated skeleton data into a set of few spatial basis of switching temporal processes. This results in a dynamical deep generative latent model that parses the meaningful intrinsic states in the dynamics of 3D pose data.
  arXiv  Detail & Related papers  (2021-06-18T23:58:49Z)
• NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go [109.88509362837475]
  We present NeuroMorph, a new neural network architecture that takes as input two 3D shapes. NeuroMorph produces smooth and point-to-point correspondences between them. It works well for a large variety of input shapes, including non-isometric pairs from different object categories.
  arXiv  Detail & Related papers  (2021-06-17T12:25:44Z)
• Flow-based Generative Models for Learning Manifold to Manifold Mappings [39.60406116984869]
  We introduce three kinds of invertible layers for manifold-valued data, which are analogous to their functionality in flow-based generative models. We show promising results where we can reliably and accurately reconstruct brain images of a field of orientation distribution functions.
  arXiv  Detail & Related papers  (2020-12-18T02:19:18Z)
• Modeling Shared Responses in Neuroimaging Studies through MultiView ICA [94.31804763196116]
  Group studies involving large cohorts of subjects are important to draw general conclusions about brain functional organization. We propose a novel MultiView Independent Component Analysis model for group studies, where data from each subject are modeled as a linear combination of shared independent sources plus noise. We demonstrate the usefulness of our approach first on fMRI data, where our model demonstrates improved sensitivity in identifying common sources among subjects.
  arXiv  Detail & Related papers  (2020-06-11T17:29:53Z)
• Dynamic multi-object Gaussian process models: A framework for data-driven functional modelling of human joints [0.0]
  A principled and robust way to combine shape and pose features has been illusive due to three main issues. We propose a new framework for dynamic multi-object statistical modelling framework for the analysis of human joints. The framework affords an efficient generative dynamic multi-object modelling platform for biological joints.
  arXiv  Detail & Related papers  (2020-01-22T07:57:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.