Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation

TL;DR

This paper introduces ACM-FD, a versatile probabilistic surrogate model based on diffusion processes, capable of multi-physics emulation, multiple tasks, and efficient conditional generation with reduced computational costs.

Contribution

It extends diffusion models with Gaussian process noise modeling and a novel loss for flexible multi-functional, conditional physics simulation, addressing previous limitations.

Findings

Effective across various multi-physics systems

Reduces computational cost via Kronecker product structure

Supports diverse tasks including forward and inverse predictions

Abstract

Modern physics simulation often involves multiple functions of interests, and traditional numerical approaches are known to be complex and computationally costly. While machine learning-based surrogate models can offer significant cost reductions, most focus on a single task, such as forward prediction, and typically lack uncertainty quantification -- an essential component in many applications. To overcome these limitations, we propose Arbitrarily-Conditioned Multi-Functional Diffusion (ACM-FD), a versatile probabilistic surrogate model for multi-physics emulation. ACM-FD can perform a wide range of tasks within a single framework, including forward prediction, various inverse problems, and simulating data for entire systems or subsets of quantities conditioned on others. Specifically, we extend the standard Denoising Diffusion Probabilistic Model (DDPM) for multi-functional generation by modeling noise as Gaussian processes (GP). We propose a random-mask based, zero-regularized denoising loss to achieve flexible and robust conditional generation. We induce a Kronecker product structure in the GP covariance matrix, substantially reducing the computational cost and enabling efficient training and sampling. We demonstrate the effectiveness of ACM-FD across several fundamental multi-physics systems.