Related papers: Physics-Informed Machine Learning of Dynamical Sys…

In this paper, we develop a neural network-based approach for time-series prediction in unknown Hamiltonian dynamical systems. Our approach leverages a surrogate model and learns the system dynamics using generalized coordinates (positions)…

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

Bayesian learning of model parameters in neural networks is important in scenarios where estimates with well-calibrated uncertainty are important. In this paper, we propose Bayesian quantized networks (BQNs), quantized neural networks…

This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric…

Data-driven approaches are increasingly popular for identifying dynamical systems due to improved accuracy and availability of sensor data. However, relying solely on data for identification does not guarantee that the identified systems…

Bayesian method is capable of capturing real world uncertainties/incompleteness and properly addressing the over-fitting issue faced by deep neural networks. In recent years, Bayesian Neural Networks (BNNs) have drawn tremendous attentions…

The new generation of galaxy surveys will provide unprecedented data allowing us to test gravity at cosmological scales. A robust cosmological analysis of the large-scale structure demands exploiting the nonlinear information encoded in the…

This paper explores the prediction of subsequent steps in H\'enon Map using various machine learning techniques. The H\'enon map, well known for its chaotic behaviour, finds applications in various fields including cryptography, image…

This paper addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring…

The effectiveness of the Physics Informed Neural Networks (PINNs) for learning the dynamics of constrained Hamiltonian systems is demonstrated using the Dirac theory of constraints for regular systems with holonomic constraints and systems…

Dynamic neural networks (DyNNs) have become viable techniques to enable intelligence on resource-constrained edge devices while maintaining computational efficiency. In many cases, the implementation of DyNNs can be sub-optimal due to its…

Heterogeneous Graph Neural Networks (HGNNs) have achieved promising results in various heterogeneous graph learning tasks, owing to their superiority in capturing the intricate relationships and diverse relational semantics inherent in…

Latent space models (LSMs) are often used to analyze dynamic (time-varying) networks that evolve in continuous time. Existing approaches to Bayesian inference for these models rely on Markov chain Monte Carlo algorithms, which cannot handle…

Markov chain Monte Carlo (MCMC) methods are a powerful but computationally expensive way of performing non-parametric Bayesian inference. MCMC proposals which utilise gradients, such as Hamiltonian Monte Carlo (HMC), can better explore the…

In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its broad potential applications across science and engineering. However, purely data-driven approaches often struggle…

In the past few years, approximate Bayesian Neural Networks (BNNs) have demonstrated the ability to produce statistically consistent posteriors on a wide range of inference problems at unprecedented speed and scale. However, any disconnect…

Varying power-infeed from converter-based generation units introduces great uncertainty on system parameters such as inertia and damping. As a consequence, system operators face increasing challenges in performing dynamic security…

Sampling from high dimensional distributions is a computational bottleneck in many scientific applications. Hamiltonian Monte Carlo (HMC), and in particular the No-U-Turn Sampler (NUTS), are widely used, yet they struggle on problems with a…

Deep neural networks (DNNs) are state-of-the-art algorithms for multiple applications, spanning from image classification to speech recognition. While providing excellent accuracy, they often have enormous compute and memory requirements.…

The recent success of deep neural network models with physical constraints (so-called, Physics-Informed Neural Networks, PINNs) has led to renewed interest in the incorporation of mechanistic information in predictive models. Statisticians…