Related papers: Controlling synchronization dynamics via physics-i…
We investigate the training of Physics-Informed Neural Networks (PINNs) from a control-theoretic perspective. Using gradient descent with resampling, we interpret the training dynamics as asymptotically equivalent to a stochastic…
Flexoelectricity, the coupling between strain gradients and electric polarization, poses significant computational challenges due to its governing fourth-order partial differential equations that require C1-continuous solutions. To address…
Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are…
We present a unified theoretical framework for analyzing the stability and consistency of Physics-Informed Neural Networks (PINNs), grounded in operator coercivity, variational formulations, and non-asymptotic perturbation theory. PINNs…
Physics-informed neural network (PINN) is a data-driven approach to solve equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory when it is used to solve multiscale equations. Homogenization…
This study introduces a unified control framework that addresses the challenge of precise quadruped locomotion with unknown payloads, named as online payload identification-based physics-informed neural network predictive control…
The integration of machine learning with domain-specific physics is transforming the design, monitoring, and control of electricity systems, where data scarcity, limited interpretability, and the need to enforce physical laws constrain…
The use of deep learning methods in scientific computing represents a potential paradigm shift in engineering problem solving. One of the most prominent developments is Physics-Informed Neural Networks (PINNs), in which neural networks are…
Synchronization is an ubiquitous phenomenon in dynamical systems of networked oscillators. While it is often a goal to achieve, in some context one would like to decrease it, e.g., although synchronization is essential to the good…
Incompressible fluid flow around a cylinder is one of the classical problems in fluid-dynamics with strong relevance with many real-world engineering problems, for example, design of offshore structures or design of a pin-fin heat…
Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…
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…
Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we…
We present a Physics-Informed Neural Network (PINN) to simulate the thermochemical evolution of a composite material on a tool undergoing cure in an autoclave. In particular, we solve the governing coupled system of differential equations…
Quantum Fisher Information (QFI) sets the ultimate precision limit for parameter estimation and is therefore a central quantity in quantum metrology. In time-dependent many-body systems, however, maximizing QFI is a highly non-trivial task…
Achieving clean combustion systems is crucial in terms of solving environmental impacts, decarbonization needs and sustainability matters. Traditional combustion modeling techniques via computational fluid dynamics with accurate chemical…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
We present a novel numerical approach aiming at computing equilibria and dynamics structures of magnetized plasmas in coronal environments. A technique based on the use of neural networks that integrates the partial differential equations…
We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations…
For Prognostics and Health Management (PHM) of Lithium-ion (Li-ion) batteries, many models have been established to characterize their degradation process. The existing empirical or physical models can reveal important information regarding…