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pADAM: A Plug-and-Play All-in-One Diffusion Architecture for Multi-Physics Learning

Year: 2026

Type: preprint

Abstract: Generalizing across disparate physical laws remains a fundamental challenge for artificial intelligence in science. Existing deep-learning solvers are largely confined to single-equation settings, limiting transfer across physical regimes and inference tasks. Here we introduce pADAM, a unified generative framework that learns a shared probabilistic prior across heterogeneous partial differential equation families. Through a learned joint distribution of system states and, where applicable, physical parameters, pADAM supports forward prediction and inverse inference within a single architecture without retraining. Across benchmarks ranging from scalar diffusion to nonlinear Navier--Stokes equations, pADAM achieves accurate inference even under sparse observations. Combined with conformal prediction, it also provides reliable uncertainty quantification with coverage guarantees. In addition, pADAM performs probabilistic model selection from only two sparse snapshots, identifying governing laws through its learned generative representation. These results highlight the potential of generative multi-physics modeling for unified and uncertainty-aware scientific inference.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2603.16757

Authors: Mollaali, Amirhossein, Kim, Bongseok, Moya, Christian, Lin, Guang

Institution: Purdue University West Lafayette

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, Division of Chemical, Bioengineering, Environmental, and Transport Systems, Division of Electrical, Communications and Cyber Systems, Advanced Scientific Computing Research

Awards: Collaborative Research: FDT-BioTech: NOURISH: Nutritional Optimization Using Real-time Integrated Sensors and Health Digital Twins, G2778948316, G3047343479, TRUSTWORTHY HETEROGENEOUS DATA-AWARE BAYESIAN FEDERATED LEARNING, G3723704744, Collaborative Research: Robust Deep Learning in Real Physical Space: Generalization, Scalability, and Credibility, Collaborative Research: Inference and Uncertainty Quantification for High Dimensional Systems in Remote Sensing: Methods, Computation, and Applications, G6355769530, ASCENT: From sensors to multiscale digital twin to autonomous operation of resilient electric power grids, Elements: FourPhonon: A Computational Tool for Higher-Order Phonon Anharmonicity and Thermal Properties, CDS&E: Integrated Molecular Dynamics and Machine Learning Investigation of Gas-Liquid Interface in Transcritical Reacting Flows

OpenAlex ID: W7139115643

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