相关论文: On Higher Order Positive Differential Energy Opera…

Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…

In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…

PDE-Constrained Optimization (PDECO) problems can be accelerated significantly by employing gradient-based methods with surrogate models like neural operators compared to traditional numerical solvers. However, this approach faces two key…

Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…

Electro-optic (EO) modulation is a well-known and essential topic in the field of communications and sensing. Its ultrahigh efficiency is unprecedentedly desired in the current green and data era. However, dramatically increasing the…

Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background…

Accurate exploration of protein conformational ensembles is essential for uncovering function but remains hard because molecular-dynamics (MD) simulations suffer from high computational costs and energy-barrier trapping. This paper presents…

Understanding whether cosmic acceleration arises from a cosmological constant or a dynamical component is a central goal of cosmology, and the Dark Energy Spectroscopic Instrument (DESI) enables stringent tests with high-precision distance…

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg…

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep…

The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…

We introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. DAOE is based on evolving observables in the Heisenberg…

We introduce MENO (''Matrix Exponential-based Neural Operator''), a hybrid surrogate modeling framework for efficiently solving stiff systems of ordinary differential equations (ODEs) that exhibit a sparse nonlinear structure. In such…

Energy-Dissipative Evolutionary Deep Operator Neural Network is an operator learning neural network. It is designed to seed numerical solutions for a class of partial differential equations instead of a single partial differential equation,…

In this work, we concern with the high order numerical methods for coupled forward-backward stochastic differential equations (FBSDEs). Based on the FBSDEs theory, we derive two reference ordinary differential equations (ODEs) from the…

Integration of nonlinear partial differential equations with the help of the non-commutative integration over octonions is studied. An apparatus permitting to take into account symmetry properties of PDOs is developed. For this purpose…

Denoising diffusion models (DDMs) have emerged as a powerful class of generative models. A forward diffusion process slowly perturbs the data, while a deep model learns to gradually denoise. Synthesis amounts to solving a differential…

This work starts with the introduction of a family of differential energy operators. Energy operators ($Psi_R^+$, $Psi_R^-$) were defined together with a method to decompose the wave equation in a previous work. Here the energy operators…

Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…

Time- and frequency resolved optical signals provide insights into the properties of light harvesting molecular complexes, including excitation energies, dipole strengths and orientations, as well as in the exciton energy flow through the…