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In this work we present a data-driven method for the discovery of parametric partial differential equations (PDEs), thus allowing one to disambiguate between the underlying evolution equations and their parametric dependencies. Group…
A preceding paper demonstrated that explicit asymptotic methods generally work much better for extremely stiff reaction networks than has previously been shown in the literature. There we showed that for systems well removed from…
Stochastic evolution equations describing the dynamics of systems under the influence of both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying these systems from sparse-in-time observations…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…
We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow-field data useful for flow analysis, reduced-order modeling, and flow control.…
In unsupervised learning, dimensionality reduction is an important tool for data exploration and visualization. Because these aims are typically open-ended, it can be useful to frame the problem as looking for patterns that are enriched in…
In this study we put forth a modular approach for distilling hidden flow physics in discrete and sparse observations. To address functional expressiblity, a key limitation of the black-box machine learning methods, we have exploited the use…
This paper presents a novel method for transient stability analysis (TSA) that circumvents the limitations of sequential numerical integration and energy functions. The proposed method begins by constructing a trajectory-dependent stability…
In this work we present a computationally efficient linear optimization approach for estimating the cross--power spectrum of an hidden multivariate stochastic process from that of another observed process. Sparsity in the resulting…
Discovering governing equations from data is crucial for understanding complex systems in many diverse fields from science to engineering. Yet, there still is a lack of versatile computational toolbox to deal with this long standing…
Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…
The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is…
Symbolic regression is a technique that can automatically derive analytic models from data. Traditionally, symbolic regression has been implemented primarily through genetic programming that evolves populations of candidate solutions…
The reconstruction and prediction of full-state flows from sparse data are of great scientific and engineering significance yet remain challenging, especially in applications where data are sparse and/or subjected to noise. To this end,…
We study large but finite neural networks that, in the thermodynamic limit, admit an exact low-dimensional mean-field description. We assume that the governing mean-field equations describing macroscopic quantities such as the mean firing…
For machine learning of interatomic potentials a scalable sparse Gaussian process regression formalism is introduced with a data-efficient on-the-fly adaptive sampling algorithm. With this approach, the computational cost is effectively…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
With the rapid advances of data acquisition techniques, spatio-temporal data are becoming increasingly abundant in a diverse array of disciplines. Here we develop spatio-temporal regression methodology for analyzing large amounts of…
Machine learning is used to generate empirical pseudopotentials that characterize the local screened interactions in the Kohn-Sham Hamiltonian. Our approach incorporates momentum-range-separated rotation-covariant descriptors to capture…
Sparse model identification enables nonlinear dynamical system discovery from data. However, the control of false discoveries for sparse model identification is challenging, especially in the low-data and high-noise limit. In this paper, we…