Related papers: Recovering implicit physics model under real-world…

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on…

Physics-informed neural networks allow models to be trained by physical laws described by general nonlinear partial differential equations. However, traditional architectures struggle to solve more challenging time-dependent problems due to…

We investigate the hydrodynamic recovery of Lattice Boltzmann Method (LBM) by analyzing exact balance relations for energy and enstrophy derived from averaging the equations of motion on sub-volumes of different sizes. In the context of 2D…

Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…

This paper focuses on developing a method to obtain an uncertain linear fractional transformation (LFT) system that adequately captures the dynamics of a nonlinear time-invariant system over some desired envelope. First, the nonlinear…

The forecasting and computation of the stability of chaotic systems from partial observations are tasks for which traditional equation-based methods may not be suitable. In this computational paper, we propose data-driven methods to (i)…

Model discovery based on existing data has been one of the major focuses of mathematical modelers for decades. Despite tremendous achievements of model identification from adequate data, how to unravel the models from limited data is less…

The widespread availability of complex time series data in various domains such as environmental science, epidemiology, and economics demands robust causal discovery methods that can identify intricate contemporaneous and lagged…

Liquid Time-Constant networks (LTCs), a type of continuous-time graph neural network, excel at modeling irregularly-sampled dynamics but are fundamentally confined to Euclidean space. This limitation introduces significant geometric…

Sparsity and missing data problems are very common in spatiotemporal traffic data collected from various sensing systems. Making accurate imputation is critical to many applications in intelligent transportation systems. In this paper, we…

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to…

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…

For multilayer materials in thin substrate systems, interfacial failure is one of the most challenges. The traction-separation relations (TSR) quantitatively describe the mechanical behavior of a material interface undergoing openings,…

We propose a physics-constrained convolutional neural network (PC-CNN) to solve two types of inverse problems in partial differential equations (PDEs), which are nonlinear and vary both in space and time. In the first inverse problem, we…

We introduce Active Tuning, a novel paradigm for optimizing the internal dynamics of recurrent neural networks (RNNs) on the fly. In contrast to the conventional sequence-to-sequence mapping scheme, Active Tuning decouples the RNN's…

Because of the internal malfunction of satellite sensors and poor atmospheric conditions such as thick cloud, the acquired remote sensing data often suffer from missing information, i.e., the data usability is greatly reduced. In this…

Regularization is critical for solving ill-posed geophysical inverse problems. Explicit regularization is often used, but there are opportunities to explore the implicit regularization effects that are inherent in a Neural Network…

This paper introduces an innovative physics-informed deep learning framework for metamodeling of nonlinear structural systems with scarce data. The basic concept is to incorporate physics knowledge (e.g., laws of physics, scientific…

This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the…

The growing availability and importance of time series data across various domains, including environmental science, epidemiology, and economics, has led to an increasing need for time-series causal discovery methods that can identify the…