4 papers
Out-of-distribution transfer of PDE foundation models to material dynamics under extreme loading
Mahindra Rautela, Alexander Most, Siddharth Mansingh +9
Most PDE foundation models are pretrained and fine-tuned on fluid-centric benchmarks. Their utility under extreme-loading material dynamics remains unclear. We benchmark out-of-dis…
MORPH: PDE Foundation Models with Arbitrary Data Modality
Mahindra Singh Rautela, Alexander Most, Siddharth Mansingh +6
We introduce MORPH, a modality-agnostic, autoregressive foundation model for partial differential equations (PDEs). MORPH is built on a convolutional vision transformer backbone th…
Towards Reasoning for PDE Foundation Models: A Reward-Model-Driven Inference-Time-Scaling Algorithm
Siddharth Mansingh, James Amarel, Ragib Arnab +10
Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have…
Generalization vs. Memorization in Autoregressive Deep Learning: Or, Examining Temporal Decay of Gradient Coherence
James Amarel, Nicolas Hengartner, Robyn Miller +8
Foundation models trained as autoregressive PDE surrogates hold significant promise for accelerating scientific discovery through their capacity to both extrapolate beyond training…