MORPH: PDE Foundation Models with Arbitrary Data Modality Article Swipe

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Mahindra Rautela , Siddharth Mansingh , Bradley C. Love , Ayan Biswas , Diane Oyen , Earl Lawrence · YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2509.21670

We introduce MORPH, a modality-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 modality (1D--3D) at different resolutions, and 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 factorize 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. 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 the 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.

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preprint

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en

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http://arxiv.org/abs/2509.21670

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https://arxiv.org/pdf/2509.21670

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https://openalex.org/W4417086271

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DOI

https://doi.org/10.48550/arxiv.2509.21670

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Title

MORPH: PDE Foundation Models with Arbitrary Data Modality

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preprint

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en

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2025

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2025-09-25

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Mahindra Rautela, Siddharth Mansingh, Bradley C. Love, Ayan Biswas, Diane Oyen, Earl Lawrence

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https://arxiv.org/abs/2509.21670

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https://arxiv.org/pdf/2509.21670

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green

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