I started in physics with numerical simulations, then accidentally found my way into ML. This Caltech SURF project let me bring those ideas back to physics beyond textbooks. The journey was nonlinear, full of surprising empirical and theoretical discoveries. Grateful for the guidance and opportunity. A formative experience at the frontier of computational physics × generative models. Prof. Anima Anandkumar (@AnimaAnandkumar) Solving Inverse PDEs with 1% Paired Data: Introducing Decoupled Diffusion Inverse Solver We propose a data-efficient and physics-aware diffusion framework for solving inverse problems on function spaces. In scientific machine learning, solving inverse problems requires costly and limited data acquisition from physical systems. Existing joint-embedding diffusion models require massive paired training data, as they represent the underlying physics implicitly through statistical correlations. In this work, we identify that under data scarcity, the observation-induced guidance signal vanishes during posterior sampling, making reconstruction impossible. Our Solution: We propose a decoupled design against joint-embedding: an unconditional diffusion learns the coefficient prior, while a neural operator explicitly models the forward PDE for guidance. This enables (1) superior data efficiency (2) effective physics-informed learning and sampling. Performance: Achieves state-of-the-art results on Navier-Stokes, Helmholtz, and Poisson benchmarks, improving spectral error by 54% on average. Data Efficiency: DDIS maintains high accuracy even when limited to just 1% of paired training data, outperforming joint models by 40% in L2 error. Robustness: Theoretical guarantees that avoid the guidance attenuation identified in joint-embedding methods. Check out the paper for the full theoretical analysis and experiments! arxiv.org/abs/2601.23280 Thomas Lin , @jiacheny7, Alex Chiang, Julius Berner, #MachineLearning #DiffusionModels #InverseProblems #PDE #NeuralOperators @Caltech #AI4Science — https://nitter.net/AnimaAnandkumar/status/2019510545242890370#m

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