arXiv:2608.31028v1 Announce Type: cross Abstract: Scientific discovery often requires reasoning over competing hypotheses that are consistent with experimental observations. For mixed-variable and co...
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.
arXiv:2610.08475v1 Announce Type: new Abstract: In many-query scenarios, data-driven surrogate models provide an efficient alternative to high-fidelity solvers for simulating physical systems governe...
arXiv:2609.38623v1 Announce Type: new Abstract: Learning partial differential equation (PDE) dynamics across varying domains is central to predictive modelling and data-driven discovery of governing...
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
arXiv:2608. 04827v1 Announce Type: cross Abstract: We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds.
arXiv:2606. 00988v1 Announce Type: new Abstract: Symbolic regression (SR) offers a route to scientific discovery by converting observations into interpretable governing equations.
We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds. While diffusion models (DMs) have achieved state-of-the-art results in high-dimensional data synthesis, they rely on large training datasets and ignore intrinsic geometric structure.
The paper introduces a new federated learning protocol for partial differential equations called solution-space PDE-Dirichlet, which transforms continuous supervised responses into reusable solution bins and measures client separation via optimal transport. It establishes an exact inverse relationship between population allocation heterogeneity and Dirichlet concentration, and shows how response heterogeneity can cause gradient disagreement, local-update dispersion, and parameter divergence. Experiments on seven PDE tasks, three neural-operator families, and five random seeds demonstrate that lower concentration consistently increases solution distance and optimization heterogeneity, with the most pronounced error increase observed in low-viscosity Burgers equations.
arXiv:2508. 09156v3 Announce Type: replace-cross Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.
arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.