arXiv:2606. 20417v1 Announce Type: new Abstract: Inverse problems for differential equations arise throughout science and engineering, where one seeks to infer unknown model parameters from noisy or incomplete observations.
arXiv:2607. 06252v1 Announce Type: cross Abstract: Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations.
arXiv:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.
arXiv:2503. 05598v2 Announce Type: replace-cross Abstract: This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation.
arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).
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. 01468v1 Announce Type: cross Abstract: Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings.
arXiv:2606. 13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning 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:2608. 09494v1 Announce Type: cross Abstract: In this paper we provide Monte Carlo and deep neural network approximations for stochastic representations of solutions to linear elliptic partial differential equations with constant diffusion, drift and killing.
arXiv:2606. 18305v1 Announce Type: cross Abstract: Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing.
arXiv:2504. 01894v2 Announce Type: replace Abstract: We present a bifidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution.