相关论文: Kinetics Parameter Optimization via Neural Ordinar…
We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…
Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…
Finding optimal reaction coordinates and predicting accurate kinetic rates for activated processes are two of the foremost challenges of molecular simulations. We introduce an algorithm that tackles the two problems at once: starting from a…
We present a novel approach (DyNODE) that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. We conduct a systematic evaluation and comparison of our method and…
Metaheuristic algorithms, widely used for solving complex non-convex and non-differentiable optimization problems, often lack a solid mathematical foundation. In this review, we explore how concepts and methods from kinetic theory can offer…
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…
Complex dynamic systems are typically either modeled using expert knowledge in the form of differential equations or via data-driven universal approximation models such as artificial neural networks (ANN). While the first approach has…
State estimation is an important aspect in many robotics applications. In this work, we consider the task of obtaining accurate state estimates for robotic systems by enhancing the dynamics model used in state estimation algorithms.…
We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Geometry optimization is an important part of both computational materials and surface science because it is the path to finding ground state atomic structures and reaction pathways. These properties are used in the estimation of…
The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…
Optimal operation of chemical processes is vital for energy, resource, and cost savings in chemical engineering. The problem of optimal operation can be tackled with reinforcement learning, but traditional reinforcement learning methods…
Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this…
In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…
Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…
Designing controllers that achieve task objectives while ensuring safety is a key challenge in control systems. This work introduces Opt-ODENet, a Neural ODE framework with a differentiable Quadratic Programming (QP) optimization layer to…
Neural Ordinary Differential Equations (NeuralODEs) present an attractive way to extract dynamical laws from time series data, as they bridge neural networks with the differential equation-based modeling paradigm of the physical sciences.…