Related papers: Neural Controlled Differential Equations with Quan…
The Schwinger Model from Quantum Electrodynamics (QED) has long served as a valuable simplified model for exploring key physical phenomena in Quantum Chromodynamics (QCD)-a field rich with fundamental insights but is substantially more…
Deep Equilibrium Model (DEQ), which serves as a typical implicit neural network, emphasizes their memory efficiency and competitive performance compared to explicit neural networks. However, there has been relatively limited theoretical…
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…
Data-driven surrogate modeling has emerged as a promising approach for reducing computational expenses of multiscale simulations. Recurrent Neural Network (RNN) is a common choice for modeling of path-dependent behavior. However, previous…
Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects…
This paper deals with neural networks as dynamical systems governed by differential or difference equations. It shows that the introduction of skip connections into network architectures, such as residual networks and dense networks, turns…
In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical…
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
Time delays are ubiquitous in industry, and they must be accounted for when designing control strategies. However, numerical optimal control (NOC) of delay differential equations (DDEs) is challenging because it requires specialized…
We construct an abstract pseudodifferential calculus with operator-valued symbol, adapted to the treatment of Coulomb-type interactions, and we apply it to study the quantum evolution of molecules in the Born-Oppenheimer approximation, in…
Nonlinear conservation laws govern a broad class of important physical systems in science and industry and are central to scientific machine learning (SciML). Large general-purpose models offer speed, but replacing the numerical and…
We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical…
In this note, variational Monte Carlo method based on neural quantum states for spin systems is reviewed. Using a neural network as the wave function allows for a more generalized expression of various types of interactions, including…
Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…
Uncertainty quantification (UQ) helps to make trustworthy predictions based on collected observations and uncertain domain knowledge. With increased usage of deep learning in various applications, the need for efficient UQ methods that can…
We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…
We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in…
Quantum dynamics, typically expressed in the form of a time-dependent Schr\"odinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, when simulating quantum dynamics that involves the emission…
Quantum confinement is studied by numerically solving time-dependent Schr\"odinger equation. An imaginary-time evolution technique is employed in conjunction with the minimization of an expectation value, to reach the global minimum.…