Related papers: Robust data driven discovery of a seismic wave equ…

Machine learning can uncover physical concepts or physical equations when prior knowledge from the other is available. However, these two aspects are often intertwined and cannot be discovered independently. We extend SciNet, which is a…

This paper presents a computational framework that generates ensemble predictive mechanics models with uncertainty quantification (UQ). We first develop a causal discovery algorithm to infer causal relations among time-history data measured…

We numerically show that a deep neural network (DNN) can learn macroscopic thermodynamic laws purely from microscopic data. Using molecular dynamics simulations, we generate the data of snapshot images of gas particles undergoing adiabatic…

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…

Data-driven discovery of partial differential equations (PDEs) has achieved considerable development in recent years. Several aspects of problems have been resolved by sparse regression-based and neural network-based methods. However, the…

Seismic wave velocity of underground rock plays important role in detecting internal structure of the Earth. Rock physics models have long been the focus of predicting wave velocity. However, construction of a theoretical model requires…

Experimental data is often comprised of variables measured independently, at different sampling rates (non-uniform ${\Delta}$t between successive measurements); and at a specific time point only a subset of all variables may be sampled.…

The data-driven approach has been demonstrated as a promising technique to solve complicated scientific problems. Full Waveform Inversion (FWI) is commonly epitomized as an image-to-image translation task, which motivates the use of deep…

Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…

Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress-strain relation.…

Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…

The discovery of conservation laws is a cornerstone of scientific progress. However, identifying these invariants from observational data remains a significant challenge. We propose a hybrid framework to automate the discovery of conserved…

In the last decade, the scientific community has devolved its attention to the deployment of data-driven approaches in scientific research to provide accurate and reliable analysis of a plethora of phenomena. Most notably, Physics-informed…

Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning…

The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…

Analog machine learning hardware platforms promise to be faster and more energy-efficient than their digital counterparts. Wave physics, as found in acoustics and optics, is a natural candidate for building analog processors for…

Machine learning models of materials$^{1-5}$ accelerate discovery compared to ab initio methods: deep learning models now reproduce density functional theory (DFT)-calculated results at one hundred thousandths of the cost of DFT$^{6}$. To…

The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…