Related papers: Equation-Free Discovery of Open Quantum Systems vi…

This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory…

Simulating open quantum systems on quantum computers presents a fundamental challenge: open quantum dynamics are intrinsically nonunitary, whereas quantum computers operate through unitary evolution. Conventional approaches overcome this…

Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the…

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

The discovery of constitutive models for hyperelastic materials is essential yet challenging due to their nonlinear behavior and the limited availability of experimental data. Traditional methods typically require extensive stress-strain or…

Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…

This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the…

In this paper, we put forward a neural network framework to solve the nonlinear hyperbolic systems. This framework, named relaxation neural networks(RelaxNN), is a simple and scalable extension of physics-informed neural networks(PINN). It…

Physics-Informed Neural Networks (PINNs) are gaining popularity as a method for solving differential equations. While being more feasible in some contexts than the classical numerical techniques, PINNs still lack credibility. A remedy for…

Quantum computing promises to provide machine learning with computational advantages. However, noisy intermediate-scale quantum (NISQ) devices pose engineering challenges to realizing quantum machine learning (QML) advantages. Recently, a…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving PDEs, yet existing uncertainty quantification (UQ) approaches for PINNs generally lack rigorous statistical guarantees. In this work, we bridge this…

This study presents a novel physics-informed neural network (PINN) framework for modeling poroelasticity in heterogeneous media with material interfaces. The approach introduces a composite neural network (CoNN) where separate neural…

With the overwhelming success in the field of quantum information in the last decades, the "quest" for a Quantum Neural Network (QNN) model began in order to combine quantum computing with the striking properties of neural computing. This…

Physics-Informed Neural Networks present a novel approach in SciML that integrates physical laws in the form of partial differential equations directly into the NN through soft constraints in the loss function. This work studies the…

We consider the learnability of the quantum neural network (QNN) built on the variational hybrid quantum-classical scheme, which remains largely unknown due to the non-convex optimization landscape, the measurement error, and the…

Data-driven discovery of governing equations in computational science has emerged as a new paradigm for obtaining accurate physical models and as a possible alternative to theoretical derivations. The recently developed physics-informed…

Physics-Informed Neural Networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs). PINNs are based on simple architectures, and learn the behavior of complex…

Physics-Informed Neural Networks (PINNs) are a novel computational approach for solving partial differential equations (PDEs) with noisy and sparse initial and boundary data. Although, efficient quantification of epistemic and aleatoric…

Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding governing physical laws directly into the training objective. Recent advances in quantum machine…

Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and…