Related papers: Schr\"{o}dingerNet: A Universal Neural Network Sol…
Neural Network Differential Equation (NN DE) solvers have surged in popularity due to a combination of factors: computational advances making their optimization more tractable, their capacity to handle high dimensional problems, easy…
We present E NERGY N ET , a new framework for analyzing and building artificial neural network architectures. Our approach adaptively learns the structure of the networks in an unsupervised manner. The methodology is based upon the…
Fermionic neural network (FermiNet) is a recently proposed wavefunction Ansatz, which is used in variational Monte Carlo (VMC) methods to solve the many-electron Schr\"{o}dinger equation. FermiNet proposes permutation-equivariant…
This work presents a direct and highly accurate method to solve ordinary differential equations, in particular the Schr\"odinger equation in one dimension, through the direct substitution of a power series solution to obtain a purely…
Machine learning with artificial neural networks (ANNs), provides solutions for the growing complexity of modern communication systems. This complexity, however, increases power consumption, making the systems energy-intensive. Spiking…
Neural networks are emerging as a powerful tool for determining the quantum states of interacting many-body fermionic systems. The standard approach trains a neural-network ansatz by minimizing the mean local energy estimated from Monte…
Neuromorphic computing and, in particular, spiking neural networks (SNNs) have become an attractive alternative to deep neural networks for a broad range of signal processing applications, processing static and/or temporal inputs from…
Physics-informed neural networks (PINNs) is becoming a popular alternative method for solving partial differential equations (PDEs). However, they require dedicated manual modifications to the hyperparameters of the network, the sampling…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
Edge AI applications increasingly require ultra-low-power, low-latency inference. Neuromorphic computing based on event-driven spiking neural networks (SNNs) offers an attractive path, but practical deployment on resource-constrained…
In optical fiber communication, system identification (SI) for the nonlinear Schr\"odinger equation (NLSE) has long been studied mainly for fiber nonlinearity compensation (NLC). One recent line of inquiry to combine a behavioral-model…
In this work, we propose a technique for the use of fermionic neural networks (FermiNets) with the Slater exponential Ansatz for electron-nuclear and electron-electron distances, which provides faster convergence of target ground-state…
More competent learning models are demanded for data processing due to increasingly greater amounts of data available in applications. Data that we encounter often have certain embedded sparsity structures. That is, if they are represented…
Full-waveform inversion problems are usually formulated as optimization problems, where the forward-wave propagation operator $f$ maps the subsurface velocity structures to seismic signals. The existing computational methods for solving…
We solve the time-dependent Schr\"odinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under…
An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the…
We present quantum algorithms for electromagnetic fields governed by Maxwell's equations. The algorithms are based on the Schr\"odingersation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system…
In the past years, artificial neural networks (ANNs) have become the de-facto standard to solve tasks in communications engineering that are difficult to solve with traditional methods. In parallel, the artificial intelligence community…
Verification of Neural Networks (NNs) that approximate the solution of Partial Differential Equations (PDEs) is a major milestone towards enhancing their trustworthiness and accelerating their deployment, especially for safety-critical…
Neural operators have emerged as powerful surrogates for partial differential equation (PDE) solvers, yet they are typically trained as monolithic models for individual PDEs, require energy-intensive GPU hardware, and must be retrained from…