相关论文: Sparsely-Supervised Data Assimilation via Physics-…

Physics-informed neural networks (PINNs) have garnered significant interest for their potential in solving partial differential equations (PDEs) that govern a wide range of physical phenomena. By incorporating physical laws into the…

Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman, particle) presuppose full knowledge of the true dynamics, which is not always satisfied in…

Data assimilation (DA) improves prediction of chaotic systems by combining model forecasts with sparse, noisy observations. Many DA methods are inherently probabilistic, but accurate probabilistic DA is often computationally expensive…

Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…

The dynamic Schr\"odinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as optimal transport problems. It consists of learning non-linear diffusion processes using efficient…

Data assimilation (DA) has increasingly emerged as a critical tool for state estimation across a wide range of applications. It is significantly challenging when the governing equations of the underlying dynamics are unknown. To this end,…

Identifying governing partial differential equations (PDEs) from noisy spatiotemporal data remains challenging due to differentiation-induced noise amplification and ambiguity from overcomplete libraries. We propose a prior-informed…

Earth system modeling presents a fundamental challenge in scientific computing: capturing complex, multiscale nonlinear dynamics in computationally efficient models while minimizing forecast errors caused by necessary simplifications. Even…

Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is a nonlinear control technique that assigns a port-Hamiltonian (pH) structure to a controlled system using a state-feedback law. While IDA-PBC has been extensively…

This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based…

Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…

A new knowledge-based and machine learning hybrid modeling approach, called conditional Gaussian neural stochastic differential equation (CGNSDE), is developed to facilitate modeling complex dynamical systems and implementing analytic…

We propose a novel learning-based surrogate data assimilation (DA) model for efficient state estimation in a limited area. Our model employs a feedforward neural network for online computation, eliminating the need for integrating…

Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty…

This paper introduces scour physics-inspired neural networks (SPINNs), a hybrid physics-data-driven framework for bridge scour prediction using deep learning. SPINNs integrate physics-based, empirical equations into deep neural networks and…

With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model…

We interpret the 4D-var data assimilation problem for a parabolic partial differential equation (PDE) in the context of optimal control and revisit the process of deriving optimality conditions for an initial control problem. This is…

Fitting nonlinear dynamical models to sparse and noisy observations is fundamentally challenging. Identifying dynamics requires data assimilation (DA) to estimate system states, but DA requires an accurate dynamical model. To break this…

Data assimilation addresses the problem of identifying plausible state trajectories of dynamical systems given noisy or incomplete observations. In geosciences, it presents challenges due to the high-dimensionality of geophysical dynamical…

Estimating time-resolved velocity and pressure fields from Particle Image Velocimetry (PIV) remains challenging due to its limited temporal resolution in many applications. Data-driven approaches that combine snapshot PIV with…