arXiv:2609.40287v1 Announce Type: new Abstract: Physics-constrained generative models aim to generate physical fields that match a target distribution and satisfy prescribed constraints. However, enf...
arXiv:2609. 18566v1 Announce Type: cross Abstract: We present a physics-informed machine learning framework based on Neural Ordinary Differential Equations that solves the holographic inverse problem: reconstructing the bulk spacetime and gauge field of a charged AdS black hole directly from boundary fermionic spectral functions.
arXiv:2606. 30117v1 Announce Type: cross Abstract: We investigate the reconstruction of holographic duals for strongly coupled quantum field theories in regimes characterized by large hierarchies and the presence of false vacua.
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.
Physics-Informed Conformal Prediction (PI‑CP) embeds PDE residuals into the nonconformity score of split conformal prediction, yielding distribution‑free prediction intervals with provable coverage that adapt spatially to physics violations. The method demonstrates consistent 89‑91% coverage across six physics scenarios, outperforming MC Dropout and Deep Ensembles, while Fourier Neural Operators (FNO) achieve superior accuracy over CNN and DeepONet. Additionally, the authors prove that FNO’s translation equivariance limits its ability to solve PDEs with Dirichlet boundary conditions, and show that adding coordinate channels can reduce error by up to 63×.
arXiv:2605. 08832v3 Announce Type: replace Abstract: Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields.
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.
The paper introduces the Latent Generative Solver (LGS), a neural PDE solver that combines a Physics VAE, a Pyramidal Flow-Forcing Transformer, and input noising to achieve generalization across twelve PDE families and stable long-term rollouts. LGS matches or surpasses deterministic baselines on one-step predictions, outperforms them on 5- and 10-step rollouts, and significantly reduces long-horizon error while cutting compute costs. It also adapts efficiently to unseen higher-resolution systems, demonstrating strong empirical performance on 2D regular-grid PDE simulations.
arXiv:2607. 27372v1 Announce Type: new Abstract: The deep learning revolution, kicked off by AlexNet, taught us that end-to-end training beats decomposing a problem into hand-designed stages.
The paper introduces GeoLAMP, a Geometry-aware Latent Autoregressive generative Model designed to solve multiphysics partial differential equations in highly irregular, micro‑scale tortuous geometries. GeoLAMP employs a dual‑encoder graph architecture to capture both global topology and fine‑scale geometry, transforms real‑space fields into compact latent representations, and uses a causal self‑attention transformer with flow matching for stable, scalable block‑wise autoregressive prediction. The model is evaluated on three benchmark datasets—reactive flow, heat convection, and elasticity—showing consistently low errors across the entire rollout horizon.
arXiv:2605.06140v3 Announce Type: replace-cross Abstract: Generative modeling of physical systems, such as molecules, requires learning distributions that are invariant under global symmetries, such...
Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support.