Related papers: Fourier Neural Differential Equations for learning…
The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…
The observation and description of collective excitations in solids is a fundamental issue when seeking to understand the physics of a many-body system. Analysis of these excitations is usually carried out by measuring the dynamical…
We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…
This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and…
We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle,…
Learning-based simulators show great potential for simulating particle dynamics when 3D groundtruth is available, but per-particle correspondences are not always accessible. The development of neural rendering presents a new solution to…
Quantum neural networks represent a new machine learning paradigm that has recently attracted much attention due to its potential promise. Under certain conditions, these models approximate the distribution of their dataset with a truncated…
Using a particular form of the quantum K-essence scalar field, we show that in the quantum formalism, a fractional differential equation in the scalar field variable, for some epochs in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) model…
Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…
Spiking Neural Networks (SNNs) draw inspiration from biological neurons to enable brain-like computation, demonstrating effectiveness in processing temporal information with energy efficiency and biological realism. Most existing SNNs are…
Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological…
High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational…
We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…
Modeling atmospheric chemistry is complex and computationally intense. Given the recent success of Deep neural networks in digital signal processing, we propose a Neural Network Emulator for fast chemical concentration modeling. We consider…
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…
We introduce a novel approach that exploits the intersection of quantum computing, machine learning and reduced density matrix functional theory to leverage the potential of quantum computing to improve simulations of interacting quantum…
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics. We approximate the…
Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…
Nonlinear time-dependent partial differential equations are essential in modeling complex phenomena across diverse fields, yet they pose significant challenges due to their computational complexity, especially in higher dimensions. This…
We present pseudo-differential enhanced physics-informed neural networks (PINNs), an extension of gradient enhancement but in Fourier space. Gradient enhancement of PINNs dictates that the PDE residual is taken to a higher differential…