Related papers: Sparsely-Supervised Data Assimilation via Physics-…

Image inpainting is an important image generation task, which aims to restore corrupted image from partial visible area. Recently, diffusion Schr\"odinger bridge methods effectively tackle this task by modeling the translation between…

Despite advances in test-time scaling and diffusion finetuning, guidance for Auto-Regressive Diffusion Models (ARDMs) remains underexplored. We introduce an amortized framework that augments a pretrained ARDM with an offline-trained…

Physics-informed deep learning (PIDL)-based models have recently garnered remarkable success in traffic state estimation (TSE). However, the prior knowledge used to guide regularization training in current mainstream architectures is based…

Prediction of the state evolution of complex high-dimensional nonlinear systems is challenging due to the nonlinear sensitivity of the evolution to small inaccuracies in the model. Data Assimilation (DA) techniques improve state estimates…

Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…

We apply two data assimilation (DA) methods, a smoother and a filter, and a model-free machine learning (ML) shallow network to forecast two weakly turbulent systems. We analyse the effect of the spatial sparsity of observations on accuracy…

Data assimilation (DA) is widely used to combine physical knowledge and observations. It is nowadays commonly used in geosciences to perform parametric calibration. In a context of climate change, old calibrations can not necessarily be…

Partial differential equations (PDEs) govern a wide range of physical systems, but solving them efficiently remains a major challenge. The idea of a scientific foundation model (SciFM) is emerging as a promising tool for learning…

Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state…

Deep learning has shown strong potential in modeling complex spatiotemporal dynamics. However, most existing methods depend on densely and uniformly sampled data, which is often unavailable in practice due to sensor and cost limitations. In…

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods…

An alternative data-driven modeling approach has been proposed and employed to gain fundamental insights into robot motion interaction with granular terrain at certain length scales. The approach is based on an integration of dimension…

Physics-informed neural networks (PINNs) provide a promising machine learning framework for solving partial differential equations, but their training often breaks down on challenging problems, sometimes converging to physically incorrect…

Developing robust data assimilation methods for hyperbolic conservation laws is a challenging subject. Those PDEs indeed show no dissipation effects and the input of additional information in the model equations may introduce errors that…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Sampling efficiently from a target unnormalized probability density remains a core challenge, with relevance across countless high-impact scientific applications. A promising approach towards this challenge is the design of amortized…

Since its introduction in 2017, physics-informed deep learning (PIDL) has garnered growing popularity in understanding the evolution of systems governed by physical laws in terms of partial differential equations (PDEs). However, empirical…

Extreme sensor sparsity makes full-field reconstruction a fundamentally ill-posed problem in scientific sensing,where the goal is to infer physical fields from sparse measurements.In this regime,the posterior is severely underconstrained…

Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations…