一个统一框架，让AI同时学习多种物理规律并做精准预测。
pADAM: A Plug-and-Play All-in-One Diffusion Architecture for Multi-Physics Learning
- 用联合概率分布统一建模不同物理方程的系统状态与参数。
- 仅需两个稀疏观测点就能识别控制方程，且预测准确率高。
- 支持正向预测与反向推断，还能提供有保证的不确定性估计。
在科学领域，跨不同物理规律进行泛化仍是人工智能的核心挑战。现有深度学习求解器多局限于单一方程场景，难以在不同物理范式间迁移或执行多种推理任务。本文提出pADAM，一个统一的生成式框架，可在异构偏微分方程族中学习共享的概率先验。通过学习系统状态及可选物理参数的联合分布，pADAM能在不重新训练的情况下，实现正向预测与逆向推断。在从标量扩散到非线性纳维-斯托克斯方程的多个基准测试中，即使在观测稀疏条件下仍能实现高精度推断。结合共形预测，该方法还能提供具有覆盖率保证的可靠不确定性量化。此外，pADAM仅需两个稀疏快照即可完成概率性模型选择，通过其生成表示识别出支配性规律。这些结果凸显了生成式多物理建模在统一、不确定感知科学推断中的潜力。
原文摘要 · Abstract (English)
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.
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