Search Results for author:
Found 89 papers, 50 papers with code
SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning
Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in environments with complicated dynamics, such as stabilizing the magnetohydrodynamics of a tokamak fusion reactor or minimizing the drag force exerted on an object in a fluid flow.
Statistical Mechanics of Dynamical System Identification
Recovering dynamical equations from observed noisy data is the central challenge of system identification.
Data-driven local operator finding for reduced-order modelling of plasma systems: I. Concept and verifications
Reduced-order plasma models that can efficiently predict plasma behavior across various settings and configurations are highly sought after yet elusive.
Data-driven local operator finding for reduced-order modelling of plasma systems: II. Application to parametric dynamics
Real-world systems often exhibit dynamics influenced by various parameters, either inherent or externally controllable, necessitating models capable of reliably capturing these parametric behaviors.
Motif distribution and function of sparse deep neural networks
We characterize the connectivity structure of feed-forward, deep neural networks (DNNs) using network motif theory.
Multi-Hierarchical Surrogate Learning for Structural Dynamical Crash Simulations Using Graph Convolutional Neural Networks
We thus propose a multi-hierarchical framework for structurally creating a series of surrogate models for a kart frame, which is a good proxy for industrial-relevant crash simulations, at different levels of resolution.
Attention for Causal Relationship Discovery from Biological Neural Dynamics
This paper explores the potential of the transformer models for learning Granger causality in networks with complex nonlinear dynamics at every node, as in neurobiological and biophysical networks.
A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learning
In this paper, we provide a unifying theoretical and methodological framework for incorporating symmetry into machine learning models in three ways: 1. enforcing known symmetry when training a model; 2. discovering unknown symmetries of a given model or data set; and 3. promoting symmetry during training by learning a model that breaks symmetries within a user-specified group of candidates when there is sufficient evidence in the data.
HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equations
Taken together, HyperSINDy offers a promising framework for model discovery and uncertainty quantification in real-world systems, integrating sparse equation discovery methods with advances in statistical machine learning and deep generative modeling.
Multi-fidelity reduced-order surrogate modeling
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given system.
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 generalizability of the Dynamic Mode Decomposition (DMD) algorithm for data-driven analysis and reduced-order modelling of plasma dynamics in cross-field ExB configurations.
Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: II. dynamics forecasting
As the OPT-DMD can be constrained to produce stable reduced-order models (ROMs) by construction, in this paper, we extend the application of the OPT-DMD and investigate the capabilities of the linear ROM from this algorithm toward forecasting in time of the plasma dynamics in configurations representative of the radial-azimuthal and axial-azimuthal cross-sections of a Hall thruster and over a range of simulation parameters in each test case.
Data-Induced Interactions of Sparse Sensors
Because of this structure, we can use just a few spatially localized sensor measurements to reconstruct the full state of a complex system.
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, forecasting and control of complex, spatio-temporal systems.
PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator
PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system.
Machine Learning for Partial Differential Equations
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation.
Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discovery
In the sparse model discovery experiment, we show that the bootstrapping-based sequential thresholding least-squares method can provide valid uncertainty quantification, converging to a delta measure centered around the true value with increased sample sizes.
Deep Learning Based Object Tracking in Walking Droplet and Granular Intruder Experiments
We present a deep-learning based tracking objects of interest in walking droplet and granular intruder experiments.
Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants
Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under $\ell_1$ constraints allows joint discoveries of governing equations and latent coordinate systems from spatio-temporal data, including simulated video frames.
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 (MAVs) is challenging, as the small scale of the robot induces large model uncertainties, demanding robust feedback controllers, while the fast dynamics and computational constraints prevent the deployment of computationally expensive strategies.
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 time-series of observations and determine when anomalous exogenous events have occurred so that relevant actions can be taken.
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-dimensional subspace.
Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects
We introduce a discrepancy modeling framework to identify the missing physics and resolve the model-measurement mismatch with two distinct approaches: (i) by learning a model for the evolution of systematic state-space residual, and (ii) by discovering a model for the deterministic dynamical error.
Dimensionally Consistent Learning with Buckingham Pi
In the absence of governing equations, dimensional analysis is a robust technique for extracting insights and finding symmetries in physical systems.
Quantifying yeast colony morphologies with feature engineering from time-lapse photography
To look at how morphology develops, we collect a dataset of time-lapse photographs of the growth of different strains of S. cerevisiae.
Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders
Here, we design a custom deep autoencoder network to learn a coordinate transformation from the delay embedded space into a new space where it is possible to represent the dynamics in a sparse, closed form.
Pruning deep neural networks generates a sparse, bio-inspired nonlinear controller for insect flight
This bio-inspired approach allows us to leverage network pruning to optimally sparsify a DNN architecture in order to perform flight tasks with as few neural connections as possible, however, there are limits to sparsification.
PySINDy: A comprehensive Python package for robust sparse system identification
Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community.
A toolkit for data-driven discovery of governing equations in high-noise regimes
Second, we propose a technique, applicable to any model discovery method based on x' = f(x), to assess the accuracy of a discovered model in the context of non-unique solutions due to noisy data.
FC2T2: The Fast Continuous Convolutional Taylor Transform with Applications in Vision and Graphics
In this paper, we revisit the Taylor series expansion from a modern Machine Learning perspective.
Robust Trimmed k-means
Clustering is a fundamental tool in unsupervised learning, used to group objects by distinguishing between similar and dissimilar features of a given data set.
Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification
The optimized DMD algorithm minimizes the model bias with a variable projection optimization, thus leading to stabilized forecasting capabilities.
Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties
Probabilistic forecasting of complex phenomena is paramount to various scientific disciplines and applications.
Learning normal form autoencoders for data-driven discovery of universal,parameter-dependent governing equations
In this work, we introduce deep learning autoencoders to discover coordinate transformations that capture the underlying parametric dependence of a dynamical system in terms of its canonical normal form, allowing for a simple representation of the parametric dependence and bifurcation structure.
Extraction of instantaneous frequencies and amplitudes in nonstationary time-series data
Time-series analysis is critical for a diversity of applications in science and engineering.
Deep Learning of Conjugate Mappings
The mapping that iterates the dynamics through consecutive intersections of the flow with the subspace is now referred to as a Poincar\'e map, and it is the primary method available for interpreting and classifying chaotic dynamics.
Modern Koopman Theory for Dynamical Systems
The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science.
PySensors: A Python Package for Sparse Sensor Placement
PySensors is a Python package for selecting and placing a sparse set of sensors for classification and reconstruction tasks.
DeepGreen: Deep Learning of Green's Functions for Nonlinear Boundary Value Problems
We find that the method succeeds on a variety of nonlinear systems including nonlinear Helmholtz and Sturm--Liouville problems, nonlinear elasticity, and a 2D nonlinear Poisson equation.
Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems
Time series forecasting remains a central challenge problem in almost all scientific disciplines.
Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Data
The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from time-series data.
Numerical differentiation of noisy data: A unifying multi-objective optimization framework
Computing derivatives of noisy measurement data is ubiquitous in the physical, engineering, and biological sciences, and it is often a critical step in developing dynamic models or designing control.
Dynamical Systems Signal Processing
Data-Driven Aerospace Engineering: Reframing the Industry with Machine Learning
Indeed, emerging methods in machine learning may be thought of as data-driven optimization techniques that are ideal for high-dimensional, non-convex, and constrained, multi-objective optimization problems, and that improve with increasing volumes of data.
Hierarchical Deep Learning of Multiscale Differential Equation Time-Steppers
Our multiscale hierarchical time-stepping scheme provides important advantages over current time-stepping algorithms, including (i) circumventing numerical stiffness due to disparate time-scales, (ii) improved accuracy in comparison with leading neural-network architectures, (iii) efficiency in long-time simulation/forecasting due to explicit training of slow time-scale dynamics, and (iv) a flexible framework that is parallelizable and may be integrated with standard numerical time-stepping algorithms.
Machine Learning and Feature Engineering for Predicting Pulse Status during Chest Compressions
Segments were collected during the 10s period of ongoing CPR prior to a pulse check, and 5s segments without CPR during the pulse check.
Bracketing brackets with bras and kets
Brackets are an essential component in aircraft manufacture and design, joining parts together, supporting weight, holding wires, and strengthening joints.
Inferring Causal Networks of Dynamical Systems through Transient Dynamics and Perturbation
Our proposed PCI method demonstrated consistently strong performance in inferring causal relations for small (2-5 node) and large (10-20 node) networks, with both linear and nonlinear dynamics.
Dynamical Systems Adaptation and Self-Organizing Systems Applications 37M10, 62D20, 62M10
Deep reinforcement learning for optical systems: A case study of mode-locked lasers
We demonstrate that deep reinforcement learning (deep RL) provides a highly effective strategy for the control and self-tuning of optical systems.
Sparse Identification of Slow Timescale Dynamics
We show that for sufficiently disparate timescales this discovered mapping can be used to discover the continuous-time slow dynamics, thus providing a novel tool for extracting dynamics on multiple timescales.
Principal component trajectories for modeling spectrally-continuous dynamics as forced linear systems
Delay embeddings of time series data have emerged as a promising coordinate basis for data-driven estimation of the Koopman operator, which seeks a linear representation for observed nonlinear dynamics.
Computational Physics Systems and Control Systems and Control
Multi-fidelity sensor selection: Greedy algorithms to place cheap and expensive sensors with cost constraints
We develop greedy algorithms to approximate the optimal solution to the multi-fidelity sensor selection problem, which is a cost constrained optimization problem prescribing the placement and number of cheap (low signal-to-noise) and expensive (high signal-to-noise) sensors in an environment or state space.
PySINDy: A Python package for the Sparse Identification of Nonlinear Dynamics from Data
PySINDy is a Python package for the discovery of governing dynamical systems models from data.
Dynamical Systems Computational Physics
Multiresolution Convolutional Autoencoders
The performance gains of this adaptive multiscale architecture are illustrated through a sequence of numerical experiments on synthetic examples and real-world spatial-temporal data.
SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics
In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities.
Deep Learning Models for Global Coordinate Transformations that Linearize PDEs
By leveraging a residual network architecture, a near-identity transformation can be exploited to encode intrinsic coordinates in which the dynamics are linear.
Learning Discrepancy Models From Experimental Data
First principles modeling of physical systems has led to significant technological advances across all branches of science.
Insect Cyborgs: Bio-mimetic Feature Generators Improve ML Accuracy on Limited Data
In this work we deploy MothNet, a computational model of the moth olfactory network, as an automatic feature generator.
Poincaré Maps for Multiscale Physics Discovery and Nonlinear Floquet Theory
Poincar\'e maps are an integral aspect to our understanding and analysis of nonlinear dynamical systems.
Dynamical Systems Chaotic Dynamics
A unified sparse optimization framework to learn parsimonious physics-informed models from data
This flexible approach can be tailored to the unique challenges associated with a wide range of applications and data sets, providing a powerful ML-based framework for learning governing models for physical systems from data.
Discovery of Physics from Data: Universal Laws and Discrepancies
Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone.
Deep Model Predictive Control with Online Learning for Complex Physical Systems
The control of complex systems is of critical importance in many branches of science, engineering, and industry.
Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data.
Money on the Table: Statistical information ignored by Softmax can improve classifier accuracy
To explore this potential resource, we develop a hybrid classifier (Softmax-Pooling Hybrid, $SPH$) that uses Softmax on high-scoring samples, but on low-scoring samples uses a log-likelihood method that pools the information from the full array $D$.
Discovering conservation laws from data for control
In this work, we formulate a data-driven architecture for discovering conserved quantities based on Koopman theory.
Insect cyborgs: Bio-mimetic feature generators improve machine learning accuracy on limited data
In this work, we deployed MothNet, a computational model of the insect olfactory network, as an automatic feature generator: Attached as a front-end pre-processor, its Readout Neurons provided new features, derived from the original features, for use by standard ML classifiers.
Deep learning of dynamics and signal-noise decomposition with time-stepping constraints
A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited.
Numerical Analysis
A Unified Framework for Sparse Relaxed Regularized Regression: SR3
We demonstrate the advantages of SR3 (computational efficiency, higher accuracy, faster convergence rates, greater flexibility) across a range of regularized regression problems with synthetic and real data, including applications in compressed sensing, LASSO, matrix completion, TV regularization, and group sparsity.
Greedy Sensor Placement with Cost Constraints
The problem of optimally placing sensors under a cost constraint arises naturally in the design of industrial and commercial products, as well as in scientific experiments.
Optimization and Control
Sparse Principal Component Analysis via Variable Projection
Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating between distinct time scales.
Diffusion Maps meet Nyström
Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems.
Putting a bug in ML: The moth olfactory network learns to read MNIST
The Moth Olfactory Network is among the simplest biological neural systems that can learn, and its architecture includes key structural elements and mechanisms widespread in biological neural nets, such as cascaded networks, competitive inhibition, high intrinsic noise, sparsity, reward mechanisms, and Hebbian plasticity.
Biological Mechanisms for Learning: A Computational Model of Olfactory Learning in the Manduca sexta Moth, with Applications to Neural Nets
From a biological perspective, the model provides a valuable tool for examining the role of neuromodulators, like octopamine, in learning, and gives insight into critical interactions between sparsity, Hebbian growth, and stimulation during learning.
Deep learning for universal linear embeddings of nonlinear dynamics
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems.
Optimized Sampling for Multiscale Dynamics
The multiresolution DMD is capable of characterizing nonlinear dynamical systems in an equation-free manner by recursively decomposing the state of the system into low-rank spatial modes and their temporal Fourier dynamics.
Dynamical Systems Numerical Analysis Data Analysis, Statistics and Probability
Predicting shim gaps in aircraft assembly with machine learning and sparse sensing
This new approach is based on the assumption that patterns exist in shim distributions across aircraft, which may be mined and used to reduce the burden of data collection and processing in future aircraft.
Sparse identification of nonlinear dynamics for model predictive control in the low-data limit
These factors limit the use of these techniques for the online identification of a model in the low-data limit, for example following an abrupt change to the system dynamics.
Optimization and Control Dynamical Systems Data Analysis, Statistics and Probability
Randomized Nonnegative Matrix Factorization
Nonnegative matrix factorization (NMF) is a powerful tool for data mining.
Deep Learning and Model Predictive Control for Self-Tuning Mode-Locked Lasers
Self-tuning optical systems are of growing importance in technological applications such as mode-locked fiber lasers.
Data-driven discovery of Koopman eigenfunctions for control
In this work, we demonstrate a data-driven control architecture, termed Koopman Reduced Order Nonlinear Identification and Control (KRONIC), that utilizes Koopman eigenfunctions to manipulate nonlinear systems using linear systems theory.
Optimization and Control Dynamical Systems
Modeling cognitive deficits following neurodegenerative diseases and traumatic brain injuries with deep convolutional neural networks
However, we provide important insight and a quantitative framework for disorders in which FAS are implicated.
Data-driven discovery of partial differential equations
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain.
Pattern Formation and Solitons
Shape Constrained Tensor Decompositions using Sparse Representations in Over-Complete Libraries
We consider $N$-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library.
Randomized Matrix Decompositions using R
The essential idea of probabilistic algorithms is to employ some amount of randomness in order to derive a smaller matrix from a high-dimensional data matrix.
Computation Mathematical Software Methodology
Compressed Dynamic Mode Decomposition for Background Modeling
We introduce the method of compressed dynamic mode decomposition (cDMD) for background modeling.
Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing physical equations from measurement data.
Dynamical Systems
Dynamic mode decomposition with control
We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems.
Optimization and Control
Selecting a Small Set of Optimal Gestures from an Extensive Lexicon
Finding the best set of gestures to use for a given computer recognition problem is an essential part of optimizing the recognition performance while being mindful to those who may articulate the gestures.
Dynamic Mode Decomposition for Real-Time Background/Foreground Separation in Video
This paper introduces the method of dynamic mode decomposition (DMD) for robustly separating video frames into background (low-rank) and foreground (sparse) components in real-time.
Low-dimensional functionality of complex network dynamics: Neuro-sensory integration in the Caenorhabditis elegans connectome
We develop a biophysical model of neuro-sensory integration in the model organism Caenorhabditis elegans.
