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

We demonstrate a deep learning framework capable of recovering physical parameters from the Nonlinear Schrodinger Equation (NLSE) under severe noise conditions. By integrating Physics-Informed Neural Networks (PINNs) with automatic…

This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…

Multi-dimensional direct numerical simulation (DNS) of the Schr\"odinger equation is needed for design and analysis of quantum nanostructures that offer numerous applications in biology, medicine, materials, electronic/photonic devices,…

This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…

Measurement of the velocity field in thermal-hydraulic experiments is of great importance for phenomena interpretation and code validation. Direct measurement employing Particle Image Velocimetry (PIV) is challenging in some multiphase…

The discovery of underlying surface partial differential equation (PDE) from observational data has significant implications across various fields, bridging the gap between theory and observation, enhancing our understanding of complex…

This work proposes a robust Partial Domain Adaptation (PDA) framework that mitigates the negative transfer problem by incorporating a robust target-supervision strategy. It leverages ensemble learning and includes diverse, complementary…

A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…

Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…

Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent…

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

Accurate estimation of long-term risk is essential for the design and analysis of stochastic dynamical systems. Existing risk quantification methods typically rely on extensive datasets involving risk events observed over extended time…

The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…

We provide a number of extensions and further interpretations of the Parameterized-Background Data-Weak (PBDW) formulation, a real-time and in-situ Data Assimilation (DA) framework for physical systems modeled by parametrized Partial…

The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…

This paper studies a coupled two-dimensional Navier--Stokes--Cahn--Hilliard phase-field model augmented by a transported auxiliary field, and develops a continuous data assimilation (CDA) framework for recovering its trajectories from…

Bridging the gap between data-rich training regimes and observation-sparse deployment conditions remains a central challenge in spatiotemporal field reconstruction, particularly when target domains exhibit distributional shifts,…

In science and engineering, machine learning techniques are increasingly successful in physical systems modeling (predicting future states of physical systems). Effectively integrating PDE loss as a constraint of system transition can…

Robust physics discovery is of great interest for many scientific and engineering fields. Inspired by the principle that a representative model is the one simplest possible, a new model selection criteria considering both model's Parsimony…

Physics-Informed Neural Networks (PINNs) have become a kind of attractive machine learning method for obtaining solutions of partial differential equations (PDEs). Training PINNs can be seen as a semi-supervised learning task, in which only…