Related papers: IDENT: Identifying Differential Equations with Num…
This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a…
Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex…
Recent advances in stochastic differential equations (SDEs) have enabled robust modeling of real-world dynamical processes across diverse domains, such as finance, health, and systems biology. However, parameter estimation for SDEs…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…
A problem of identification of piecewise-constant unknown parameters of a linear regression equation (LRE) is considered. Such parameters change their values over the interval of the regressor finite (rather than persistent) excitation. To…
Despite extensive research, time series classification and forecasting on noisy data remain highly challenging. The main difficulties lie in finding suitable mathematical concepts to describe time series and effectively separate noise from…
Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat conduction to quantum mechanical systems. Despite their…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the…
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…
Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators. In this work we perform symbolic discovery of differential…
We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…
Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by…
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…
Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast…
Perception of time from sequentially acquired sensory inputs is rooted in everyday behaviors of individual organisms. Yet, most algorithms for time-series modeling fail to learn dynamics of random event timings directly from visual or audio…
Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…
Partial differential equations (PDEs) are commonly employed to model complex industrial systems characterized by multivariable dependence. Existing physics-informed neural networks (PINNs) excel in solving PDEs in a homogeneous medium.…