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Found 70 papers, 37 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.
Koopman-Assisted Reinforcement Learning
In particular, the Koopman operator is able to capture the expectation of the time evolution of the value function of a given system via linear dynamics in the lifted coordinates.
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.
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.
Uncovering wall-shear stress dynamics from neural-network enhanced fluid flow measurements
Friction drag from a turbulent fluid moving past or inside an object plays a crucial role in domains as diverse as transportation, public utility infrastructure, energy technology, and human health.
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.
Constrained optimization of sensor placement for nuclear digital twins
Strategically placing sensors within defined spatial constraints is essential for the reconstruction of reactor flow fields and the creation of nuclear digital twins.
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.
The transformative potential of machine learning for experiments in fluid mechanics
The field of machine learning has rapidly advanced the state of the art in many fields of science and engineering, including experimental fluid dynamics, which is one of the original big-data disciplines.
Benchmarking sparse system identification with low-dimensional chaos
Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy.
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.
Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning
We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs).
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.
Swarm Modelling with Dynamic Mode Decomposition
Modelling biological or engineering swarms is challenging due to the inherently high dimension of the system, despite the often low-dimensional emergent dynamics.
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.
Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning
The complexity of real-world geophysical systems is often compounded by the fact that the observed measurements depend on hidden variables.
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.
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.
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.
Deeptime: a Python library for machine learning dynamical models from time series data
Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics.
Enhancing Computational Fluid Dynamics with Machine Learning
Machine learning is rapidly becoming a core technology for scientific computing, with numerous opportunities to advance the field of computational fluid dynamics.
Applying Machine Learning to Study Fluid Mechanics
This paper provides a short overview of how to use machine learning to build data-driven models in fluid mechanics.
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.
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.
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.
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.
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.
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.
Physics-constrained, low-dimensional models for MHD: First-principles and data-driven approaches
Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, and data-driven models, obtained by modern machine learning and system identification, can furnish this gap in the lower levels of the model hierarchy.
Computational Physics Fluid Dynamics Plasma Physics
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.
From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction
We propose spectral methods for long-term forecasting of temporal signals stemming from linear and nonlinear quasi-periodic dynamical systems.
Data-driven nonlinear aeroelastic models of morphing wings for control
Accurate and efficient aeroelastic models are critically important for enabling the optimization and control of highly flexible aerospace structures, which are expected to become pervasive in future transportation and energy systems.
Fluid Dynamics Optimization and Control
Learning Precisely Timed Feedforward Control of the Sensor-Denied Inverted Pendulum
In this work, we investigate biologically inspired strategies to develop precisely timed feedforward control laws for engineered systems with large time delays.
Systems and Control Systems and Control
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.
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.
RetinaMatch: Efficient Template Matching of Retina Images for Teleophthalmology
To the best of our knowledge, this is the first template matching algorithm for retina images with small template images from unconstrained retinal areas.
Discovering conservation laws from data for control
In this work, we formulate a data-driven architecture for discovering conserved quantities based on Koopman theory.
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.
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
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
Modal Analysis of Fluid Flows: An Overview
Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features.
Fluid Dynamics
Sparse-TDA: Sparse Realization of Topological Data Analysis for Multi-Way Classification
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples.
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
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
