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09/01/2023
Multi-fidelity reduced-order surrogate modeling
High-fidelity numerical simulations of partial differential equations (P...
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08/26/2023
Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: II. dynamics forecasting
In part I of the article, we demonstrated that a variant of the Dynamic ...
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08/26/2023
Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: I. Extraction of spatiotemporally coherent patterns
In this two-part article, we evaluate the utility and the generalizabili...
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08/08/2023
Nonlinear parametric models of viscoelastic fluid flows
Reduced-order models have been widely adopted in fluid mechanics, partic...
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07/21/2023
Data-Induced Interactions of Sparse Sensors
Large-dimensional empirical data in science and engineering frequently h...
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07/20/2023
Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstruction
Sensing is one of the most fundamental tasks for the monitoring, forecas...
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06/22/2023
PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator
PyKoopman is a Python package for the data-driven approximation of the K...
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03/30/2023
Machine Learning for Partial Differential Equations
Partial differential equations (PDEs) are among the most universal and p...
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01/30/2023
Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discovery
Sparse model identification enables nonlinear dynamical system discovery...
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11/19/2022
Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants
Recent progress in autoencoder-based sparse identification of nonlinear ...
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09/20/2022
Robust, High-Rate Trajectory Tracking on Insect-Scale Soft-Actuated Aerial Robots with Deep-Learned Tube MPC
Accurate and agile trajectory tracking in sub-gram Micro Aerial Vehicles...
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09/18/2022
Koopman-theoretic Approach for Identification of Exogenous Anomalies in Nonstationary Time-series Data
In many scenarios, it is necessary to monitor a complex system via a tim...
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05/12/2022
The Experimental Multi-Arm Pendulum on a Cart: A Benchmark System for Chaos, Learning, and Control
The single, double, and triple pendulum has served as an illustrative ex...
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04/07/2022
Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data
High-dimensional spatio-temporal dynamics can often be encoded in a low-...
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03/10/2022
Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects
Physics-based and first-principles models pervade the engineering and ph...
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02/09/2022
Dimensionally Consistent Learning with Buckingham Pi
In the absence of governing equations, dimensional analysis is a robust ...
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01/13/2022
Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders
A central challenge in data-driven model discovery is the presence of hi...
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01/04/2022
A new approach for determining optimal placement of PM2.5 air quality sensors: case study for the contiguous United States
Considerable financial resources are allocated for measuring ambient air...
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12/08/2021
Physics-informed dynamic mode decomposition (piDMD)
In this work, we demonstrate how physical principles – such as symmetrie...
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11/22/2021
Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control
Sparse model identification enables the discovery of nonlinear dynamical...
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11/12/2021
PySINDy: A comprehensive Python package for robust sparse system identification
Automated data-driven modeling, the process of directly discovering the ...
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11/08/2021
A toolkit for data-driven discovery of governing equations in high-noise regimes
We consider the data-driven discovery of governing equations from time-s...
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10/29/2021
FC2T2: The Fast Continuous Convolutional Taylor Transform with Applications in Vision and Graphics
Series expansions have been a cornerstone of applied mathematics and eng...
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08/16/2021
Robust Trimmed k-means
Clustering is a fundamental tool in unsupervised learning, used to group...
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07/22/2021
Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification
Dynamic mode decomposition (DMD) provides a regression framework for ada...
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06/10/2021
Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties
Probabilistic forecasting of complex phenomena is paramount to various s...
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06/09/2021
Learning normal form autoencoders for data-driven discovery of universal,parameter-dependent governing equations
Complex systems manifest a small number of instabilities and bifurcation...
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04/03/2021
Extraction of instantaneous frequencies and amplitudes in nonstationary time-series data
Time-series analysis is critical for a diversity of applications in scie...
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04/01/2021
Deep Learning of Conjugate Mappings
Despite many of the most common chaotic dynamical systems being continuo...
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02/24/2021
Modern Koopman Theory for Dynamical Systems
The field of dynamical systems is being transformed by the mathematical ...
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12/31/2020
DeepGreen: Deep Learning of Green's Functions for Nonlinear Boundary Value Problems
Boundary value problems (BVPs) play a central role in the mathematical a...
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10/08/2020
Dynamic mode decomposition for forecasting and analysis of power grid load data
Time series forecasting remains a central challenge problem in almost al...
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08/24/2020
Data-Driven Aerospace Engineering: Reframing the Industry with Machine Learning
Data science, and machine learning in particular, is rapidly transformin...
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08/22/2020
Hierarchical Deep Learning of Multiscale Differential Equation Time-Steppers
Nonlinear differential equations rarely admit closed-form solutions, thu...
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06/23/2020
Inferring Causal Networks of Dynamical Systems through Transient Dynamics and Perturbation
Inferring causal relations from time series measurements is an ill-posed...
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05/19/2020
SINDy-BVP: Sparse Identification of Nonlinear Dynamics for Boundary Value Problems
We develop a data-driven model discovery and system identification techn...
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04/10/2020
Multiresolution Convolutional Autoencoders
We propose a multi-resolution convolutional autoencoder (MrCAE) architec...
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04/05/2020
SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics
Accurately modeling the nonlinear dynamics of a system from measurement ...
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11/07/2019
Deep Learning Models for Global Coordinate Transformations that Linearize PDEs
We develop a deep autoencoder architecture that can be used to find a co...
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09/18/2019
Learning Discrepancy Models From Experimental Data
First principles modeling of physical systems has led to significant tec...
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06/25/2019
A unified sparse optimization framework to learn parsimonious physics-informed models from data
Machine learning (ML) is redefining what is possible in data-intensive f...
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06/19/2019
Discovery of Physics from Data: Universal Laws and Discrepancy Models
Machine learning (ML) and artificial intelligence (AI) algorithms are no...
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05/24/2019
Deep Model Predictive Control with Online Learning for Complex Physical Systems
The control of complex systems is of critical importance in many branche...
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03/25/2019
Dynamic mode decomposition for multiscale nonlinear physics
We present a data-driven method for separating complex, multiscale syste...
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03/25/2019
Data-driven multiscale decompositions for forecasting and model discovery
We present a data-driven method for separating complex, multiscale syste...
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02/20/2019
Shallow Learning for Fluid Flow Reconstruction with Limited Sensors and Limited Data
In many applications, it is important to reconstruct a fluid flow field,...
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01/26/2019
Money on the Table: Statistical information ignored by Softmax can improve classifier accuracy
Softmax is a standard final layer used in Neural Nets (NNs) to summarize...
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11/02/2018
Discovering conservation laws from data for control
Conserved quantities, i.e. constants of motion, are critical for charact...
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08/23/2018
Insect cyborgs: Biological feature generators improve machine learning accuracy on limited data
Despite many successes, machine learning (ML) methods such as neural net...
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07/14/2018