Related papers: MORPH: PDE Foundation Models with Arbitrary Data M…

We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…

Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across diverse equation families. However, existing multi-operator…

Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…

Partial differential equations (PDEs) play a central role in describing many physical phenomena. Various scientific and engineering applications demand a versatile and differentiable PDE solver that can quickly generate solutions with…

This paper introduces the Mechacnially prOgrammed Radius-adjustable PHysical (MORPH) wheel, a fully passive variable-radius wheel that embeds mechanical behavior logic for torque-responsive transformation. Unlike conventional variable…

Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

We introduce MORPH, a method for co-optimization of hardware design parameters and control policies in simulation using reinforcement learning. Like most co-optimization methods, MORPH relies on a model of the hardware being optimized,…

PDE foundation models are typically pretrained on large, diverse corpora of PDE datasets and can be adapted to new settings with limited task-specific data. However, most downstream evaluations focus on forward problems, such as…

We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the underlying PDE, we seek to approximate the evolution operator of…

Representation learning on multi-omics data is challenging due to extreme dimensionality, modality heterogeneity, and cohort-specific batch effects. While pre-trained transformer backbones have shown broad generalization capabilities in…

Partial differential equations (PDEs) govern a wide range of physical phenomena, but their numerical solution remains computationally demanding, especially when repeated simulations are required across many parameter settings. Recent…

This paper introduces PDEformer-1, a versatile neural solver capable of simultaneously addressing various partial differential equations (PDEs). With the PDE represented as a computational graph, we facilitate the seamless integration of…

Recent advances in language and vision have demonstrated that scaling up model capacity consistently improves performance across diverse tasks. In 3D visual geometry reconstruction, large-scale training has likewise proven effective for…

Healthcare data now span EHRs, medical imaging, genomics, and wearable sensors, but most diagnostic models still process these modalities in isolation. This limits their ability to capture early, cross-modal disease signatures. This paper…

Learning solution operators for partial differential equations (PDEs) has become a foundational task in scientific machine learning. However, existing neural operator methods require abundant training data for each specific PDE and lack the…

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and…

We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from…

Foundational models are trained on extensive datasets to capture the general trends of a domain. However, in medical imaging, the scarcity of data makes pre-training for every domain, modality, or task challenging. Instead of building…

A data-driven parametric model order reduction (MOR) method using a deep artificial neural network is proposed. The present network, which is the least-squares hierarchical variational autoencoder (LSH-VAE), is capable of performing…