Related papers: Sparse Symplectically Integrated Neural Networks
Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning framework based on deterministic number-theoretic sampling…
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…
Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…
We introduce semi-parametric inducing point networks (SPIN), a general-purpose architecture that can query the training set at inference time in a compute-efficient manner. Semi-parametric architectures are typically more compact than…
The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…
Hamiltonian matrix prediction is pivotal in computational chemistry, serving as the foundation for determining a wide range of molecular properties. While SE(3) equivariant graph neural networks have achieved remarkable success in this…
Sparse identification of nonlinear dynamics (SINDy) has been widely used to discover the governing equations of a dynamical system from data. It uses sparse regression techniques to identify parsimonious models of unknown systems from a…
This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using…
Model compression is significant for the wide adoption of Recurrent Neural Networks (RNNs) in both user devices possessing limited resources and business clusters requiring quick responses to large-scale service requests. This work aims to…
In this article, we propose a novel Stabilized Physics Informed Neural Networks method (SPINNs) for solving wave equations. In general, this method not only demonstrates theoretical convergence but also exhibits higher efficiency compared…
There has been an increasing interest in integrating physics knowledge and machine learning for modeling dynamical systems. However, very limited studies have been conducted on seismic wave modeling tasks. A critical challenge is that these…
Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations…
There has been a growing interest in the use of Deep Neural Networks (DNNs) to solve Partial Differential Equations (PDEs). Despite the promise that such approaches hold, there are various aspects where they could be improved. Two such…
Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal…
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…
Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…
In order to extract governing equations from time-series data, various approaches are proposed. Among those, sparse identification of nonlinear dynamics (SINDy) stands out as a successful method capable of modeling governing equations with…