一个模型搞定多物理模拟的正反问题，还能量化不确定性。
Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation
- 用高斯过程建模噪声，实现条件生成的灵活控制
- 通过克罗内克积结构降低计算成本，支持高效训练与采样
- 适合需要多任务、带不确定性的物理系统仿真研究者
现代物理模拟常涉及多个关注功能，传统数值方法复杂且计算成本高。基于机器学习的代理模型虽能显著降低成本，但多数仅针对单一任务（如正向预测），且普遍缺乏不确定性量化——这在许多应用中至关重要。为此，我们提出任意条件多功能扩散模型（ACM-FD），一种通用的概率代理模型，用于多物理系统模拟。ACM-FD可在同一框架内完成多种任务，包括正向预测、各类逆问题，以及在其他变量条件下对完整系统或子集变量进行数据模拟。具体而言，我们将标准去噪扩散概率模型（DDPM）扩展为多任务生成模型，通过将噪声建模为高斯过程（GP）实现。提出基于随机掩码的零正则化去噪损失，以实现灵活且鲁棒的条件生成。同时，在GP协方差矩阵中引入克罗内克积结构，大幅降低计算开销，实现高效的训练与采样。我们在多个基础多物理系统上验证了ACM-FD的有效性。
原文摘要 · Abstract (English)
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.
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