2025
|
Wu, Shiqi; Meunier, Gerard; Chadebec, Olivier; Li, Qianxiao; Chamoin, Ludovic Learning Dynamics of Nonlinear Field-Circuit Coupled Problems With a
Physics-Data Combined Model INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 126 (5), 2025, DOI: 10.1002/nme.70015. Abstract | BibTeX | Endnote @article{WOS:001436955800001,
title = {Learning Dynamics of Nonlinear Field-Circuit Coupled Problems With a
Physics-Data Combined Model},
author = {Shiqi Wu and Gerard Meunier and Olivier Chadebec and Qianxiao Li and Ludovic Chamoin},
doi = {10.1002/nme.70015},
times_cited = {0},
issn = {0029-5981},
year = {2025},
date = {2025-03-01},
journal = {INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING},
volume = {126},
number = {5},
publisher = {WILEY},
address = {111 RIVER ST, HOBOKEN 07030-5774, NJ USA},
abstract = {This work introduces a combined model that integrates a linear
state-space model with a Koopman-type machine-learning model to
efficiently predict the dynamics of nonlinear, high-dimensional, and
field-circuit coupled systems, as encountered in areas such as
electromagnetic compatibility, power electronics, and electric machines.
Using an extended nonintrusive model combination algorithm, the proposed
model achieves high accuracy with an error of approximately 1%,
outperforming baselines: a state-space model and a purely data-driven
model. Moreover, it delivers a computational speed-up of three orders of
magnitude compared with the traditional time-stepping volume integral
method on the same mesh in the online prediction stage, at the cost of a
one-time training effort and previously mentioned error, making it
highly effective for real-time and repeated predictions.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
This work introduces a combined model that integrates a linear
state-space model with a Koopman-type machine-learning model to
efficiently predict the dynamics of nonlinear, high-dimensional, and
field-circuit coupled systems, as encountered in areas such as
electromagnetic compatibility, power electronics, and electric machines.
Using an extended nonintrusive model combination algorithm, the proposed
model achieves high accuracy with an error of approximately 1%,
outperforming baselines: a state-space model and a purely data-driven
model. Moreover, it delivers a computational speed-up of three orders of
magnitude compared with the traditional time-stepping volume integral
method on the same mesh in the online prediction stage, at the cost of a
one-time training effort and previously mentioned error, making it
highly effective for real-time and repeated predictions. - FNClarivate Analytics Web of Science
- VR1.0
- PTJ
- AFShiqi Wu
Gerard Meunier
Olivier Chadebec
Qianxiao Li
Ludovic Chamoin
- TILearning Dynamics of Nonlinear Field-Circuit Coupled Problems With a
Physics-Data Combined Model - SOINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
- DTArticle
- ABThis work introduces a combined model that integrates a linear
state-space model with a Koopman-type machine-learning model to
efficiently predict the dynamics of nonlinear, high-dimensional, and
field-circuit coupled systems, as encountered in areas such as
electromagnetic compatibility, power electronics, and electric machines.
Using an extended nonintrusive model combination algorithm, the proposed
model achieves high accuracy with an error of approximately 1%,
outperforming baselines: a state-space model and a purely data-driven
model. Moreover, it delivers a computational speed-up of three orders of
magnitude compared with the traditional time-stepping volume integral
method on the same mesh in the online prediction stage, at the cost of a
one-time training effort and previously mentioned error, making it
highly effective for real-time and repeated predictions. - Z90
- PUWILEY
- PA111 RIVER ST, HOBOKEN 07030-5774, NJ USA
- SN0029-5981
- VL126
- DI10.1002/nme.70015
- UTWOS:001436955800001
- ER
- EF
|
Li, Qianxiao; Lin, Ting; Shen, Zuowei ON THE UNIVERSAL APPROXIMATION PROPERTY OF DEEP FULLY CONVOLUTIONAL
NEURAL NETWORKS SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 57 (5), pp. 5275-5302, 2025, DOI: 10.1137/23M1570119. Abstract | BibTeX | Endnote @article{WOS:001589086500019,
title = {ON THE UNIVERSAL APPROXIMATION PROPERTY OF DEEP FULLY CONVOLUTIONAL
NEURAL NETWORKS},
author = {Qianxiao Li and Ting Lin and Zuowei Shen},
doi = {10.1137/23M1570119},
times_cited = {0},
issn = {0036-1410},
year = {2025},
date = {2025-01-01},
journal = {SIAM JOURNAL ON MATHEMATICAL ANALYSIS},
volume = {57},
number = {5},
pages = {5275-5302},
publisher = {SIAM PUBLICATIONS},
address = {3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA},
abstract = {We study the approximation of shift-invariant or equivariant functions
by deep fully convolutional networks from the dynamical systems
perspective. We prove that deep residual fully convolutional networks
and their continuous-layer counterparts can achieve universal
approximation of these symmetric functions at constant channel width.
Moreover, we show that the same can be achieved by nonresidual variants
with at least two channels in each layer and convolutional kernel size
of at least 2. In addition, we show that these requirements are
necessary in the sense that networks with fewer channels or smaller
kernels fail to be universal approximators.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We study the approximation of shift-invariant or equivariant functions
by deep fully convolutional networks from the dynamical systems
perspective. We prove that deep residual fully convolutional networks
and their continuous-layer counterparts can achieve universal
approximation of these symmetric functions at constant channel width.
Moreover, we show that the same can be achieved by nonresidual variants
with at least two channels in each layer and convolutional kernel size
of at least 2. In addition, we show that these requirements are
necessary in the sense that networks with fewer channels or smaller
kernels fail to be universal approximators. - FNClarivate Analytics Web of Science
- VR1.0
- PTJ
- AFQianxiao Li
Ting Lin
Zuowei Shen
- TION THE UNIVERSAL APPROXIMATION PROPERTY OF DEEP FULLY CONVOLUTIONAL
NEURAL NETWORKS - SOSIAM JOURNAL ON MATHEMATICAL ANALYSIS
- DTArticle
- ABWe study the approximation of shift-invariant or equivariant functions
by deep fully convolutional networks from the dynamical systems
perspective. We prove that deep residual fully convolutional networks
and their continuous-layer counterparts can achieve universal
approximation of these symmetric functions at constant channel width.
Moreover, we show that the same can be achieved by nonresidual variants
with at least two channels in each layer and convolutional kernel size
of at least 2. In addition, we show that these requirements are
necessary in the sense that networks with fewer channels or smaller
kernels fail to be universal approximators. - Z90
- PUSIAM PUBLICATIONS
- PA3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA
- SN0036-1410
- VL57
- BP5275
- EP5302
- DI10.1137/23M1570119
- UTWOS:001589086500019
- ER
- EF
|
Zhao, Jiaxi; Li, Qianxiao MITIGATING DISTRIBUTION SHIFT IN MACHINE LEARNING--AUGMENTED HYBRID
SIMULATION SIAM JOURNAL ON SCIENTIFIC COMPUTING, 47 (2), pp. C475-C500, 2025, DOI: 10.1137/23M1615425. Abstract | BibTeX | Endnote @article{WOS:001479956800004,
title = {MITIGATING DISTRIBUTION SHIFT IN MACHINE LEARNING--AUGMENTED HYBRID
SIMULATION},
author = {Jiaxi Zhao and Qianxiao Li},
doi = {10.1137/23M1615425},
times_cited = {0},
issn = {1064-8275},
year = {2025},
date = {2025-01-01},
journal = {SIAM JOURNAL ON SCIENTIFIC COMPUTING},
volume = {47},
number = {2},
pages = {C475-C500},
publisher = {SIAM PUBLICATIONS},
address = {3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA},
abstract = {We study the problem of distribution shift generally arising in machine
learning-augmented hybrid simulation, where parts of simulation
algorithms are replaced by data-driven surrogates. A mathematical
framework is established to understand the structure of machine
learning-augmented hybrid simulation problems and the cause and effect
of the associated distribution shift. We show correlations between
distribution shift and simulation error both numerically and
theoretically. Then we propose a simple methodology based on a
tangent-space regularized estimator to control the distribution shift,
thereby improving the long-term accuracy of the simulation results. In
the linear dynamics case, we provide a thorough theoretical analysis to
quantify the effectiveness of the proposed method. Moreover, we conduct
several numerical experiments, including simulating a partially known
reaction-diffusion equation and solving Navier--Stokes equations using
the projection method with a data-driven pressure solver. In all cases,
we observe marked improvements in simulation accuracy under the proposed
method, especially for systems with high degrees of distribution shift,
such as those with relatively strong nonlinear reaction mechanisms, or
flows at large Reynolds numbers.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We study the problem of distribution shift generally arising in machine
learning-augmented hybrid simulation, where parts of simulation
algorithms are replaced by data-driven surrogates. A mathematical
framework is established to understand the structure of machine
learning-augmented hybrid simulation problems and the cause and effect
of the associated distribution shift. We show correlations between
distribution shift and simulation error both numerically and
theoretically. Then we propose a simple methodology based on a
tangent-space regularized estimator to control the distribution shift,
thereby improving the long-term accuracy of the simulation results. In
the linear dynamics case, we provide a thorough theoretical analysis to
quantify the effectiveness of the proposed method. Moreover, we conduct
several numerical experiments, including simulating a partially known
reaction-diffusion equation and solving Navier--Stokes equations using
the projection method with a data-driven pressure solver. In all cases,
we observe marked improvements in simulation accuracy under the proposed
method, especially for systems with high degrees of distribution shift,
such as those with relatively strong nonlinear reaction mechanisms, or
flows at large Reynolds numbers. - FNClarivate Analytics Web of Science
- VR1.0
- PTJ
- AFJiaxi Zhao
Qianxiao Li
- TIMITIGATING DISTRIBUTION SHIFT IN MACHINE LEARNING--AUGMENTED HYBRID
SIMULATION - SOSIAM JOURNAL ON SCIENTIFIC COMPUTING
- DTArticle
- ABWe study the problem of distribution shift generally arising in machine
learning-augmented hybrid simulation, where parts of simulation
algorithms are replaced by data-driven surrogates. A mathematical
framework is established to understand the structure of machine
learning-augmented hybrid simulation problems and the cause and effect
of the associated distribution shift. We show correlations between
distribution shift and simulation error both numerically and
theoretically. Then we propose a simple methodology based on a
tangent-space regularized estimator to control the distribution shift,
thereby improving the long-term accuracy of the simulation results. In
the linear dynamics case, we provide a thorough theoretical analysis to
quantify the effectiveness of the proposed method. Moreover, we conduct
several numerical experiments, including simulating a partially known
reaction-diffusion equation and solving Navier--Stokes equations using
the projection method with a data-driven pressure solver. In all cases,
we observe marked improvements in simulation accuracy under the proposed
method, especially for systems with high degrees of distribution shift,
such as those with relatively strong nonlinear reaction mechanisms, or
flows at large Reynolds numbers. - Z90
- PUSIAM PUBLICATIONS
- PA3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA
- SN1064-8275
- VL47
- BPC475
- EPC500
- DI10.1137/23M1615425
- UTWOS:001479956800004
- ER
- EF
|
Cheng, Jingpu; Li, Qianxiao; Lin, Ting; Shen, Zuowei INTERPOLATION, APPROXIMATION, AND CONTROLLABILITY OF DEEP NEURAL
NETWORKS SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 63 (1), pp. 625-649, 2025, DOI: 10.1137/23M1599744. Abstract | BibTeX | Endnote @article{WOS:001532779400017,
title = {INTERPOLATION, APPROXIMATION, AND CONTROLLABILITY OF DEEP NEURAL
NETWORKS},
author = {Jingpu Cheng and Qianxiao Li and Ting Lin and Zuowei Shen},
doi = {10.1137/23M1599744},
times_cited = {6},
issn = {0363-0129},
year = {2025},
date = {2025-01-01},
journal = {SIAM JOURNAL ON CONTROL AND OPTIMIZATION},
volume = {63},
number = {1},
pages = {625-649},
publisher = {SIAM PUBLICATIONS},
address = {3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA},
abstract = {We investigate the expressive power of deep residual neural networks
idealized as continuous dynamical systems through control theory.
Specifically, we consider two properties that arise from supervised
learning, namely universal interpolation---the ability to match
arbitrary input and target training samples---and the closely related
notion of universal approximation---the ability to approximate
input-target functional relationships via flow maps. Under the
assumption of affine invariance of the control family, we give a
characterization of universal interpolation, showing that it holds for
essentially any architecture with nonlinearity. Furthermore, we
elucidate the relationship between universal interpolation and universal
approximation in the context of general control systems, showing that
the two properties cannot be deduced from each other. At the same time,
we identify conditions on the control family and the target function
that ensure the equivalence of the two notions.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We investigate the expressive power of deep residual neural networks
idealized as continuous dynamical systems through control theory.
Specifically, we consider two properties that arise from supervised
learning, namely universal interpolation---the ability to match
arbitrary input and target training samples---and the closely related
notion of universal approximation---the ability to approximate
input-target functional relationships via flow maps. Under the
assumption of affine invariance of the control family, we give a
characterization of universal interpolation, showing that it holds for
essentially any architecture with nonlinearity. Furthermore, we
elucidate the relationship between universal interpolation and universal
approximation in the context of general control systems, showing that
the two properties cannot be deduced from each other. At the same time,
we identify conditions on the control family and the target function
that ensure the equivalence of the two notions. - FNClarivate Analytics Web of Science
- VR1.0
- PTJ
- AFJingpu Cheng
Qianxiao Li
Ting Lin
Zuowei Shen
- TIINTERPOLATION, APPROXIMATION, AND CONTROLLABILITY OF DEEP NEURAL
NETWORKS - SOSIAM JOURNAL ON CONTROL AND OPTIMIZATION
- DTArticle
- ABWe investigate the expressive power of deep residual neural networks
idealized as continuous dynamical systems through control theory.
Specifically, we consider two properties that arise from supervised
learning, namely universal interpolation---the ability to match
arbitrary input and target training samples---and the closely related
notion of universal approximation---the ability to approximate
input-target functional relationships via flow maps. Under the
assumption of affine invariance of the control family, we give a
characterization of universal interpolation, showing that it holds for
essentially any architecture with nonlinearity. Furthermore, we
elucidate the relationship between universal interpolation and universal
approximation in the context of general control systems, showing that
the two properties cannot be deduced from each other. At the same time,
we identify conditions on the control family and the target function
that ensure the equivalence of the two notions. - Z96
- PUSIAM PUBLICATIONS
- PA3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA
- SN0363-0129
- VL63
- BP625
- EP649
- DI10.1137/23M1599744
- UTWOS:001532779400017
- ER
- EF
|
Guo, Yue; Korda, Milan; Kevrekidis, Ioannis G; Li, Qianxiao Learning Parametric Koopman Decompositions for Prediction and Control SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 24 (1), pp. 744-781, 2025, DOI: 10.1137/23M1604576. Abstract | BibTeX | Endnote @article{WOS:001447232500010,
title = {Learning Parametric Koopman Decompositions for Prediction and Control},
author = {Yue Guo and Milan Korda and Ioannis G Kevrekidis and Qianxiao Li},
doi = {10.1137/23M1604576},
times_cited = {0},
issn = {1536-0040},
year = {2025},
date = {2025-01-01},
journal = {SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS},
volume = {24},
number = {1},
pages = {744-781},
publisher = {SIAM PUBLICATIONS},
address = {3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA},
abstract = {We present an approach to constructing approximate Koopman-type
decompositions for dynamical systems depending on static or time-varying
parameters. Our method simultaneously constructs an invariant subspace
and a parametric family of projected Koopman operators acting on this
subspace. We parametrize both the projected Koopman operator family and
the dictionary that spans the invariant subspace by neural networks, and
jointly train them with trajectory data. We show theoretically the
validity of our approach and demonstrate via numerical experiments that
it exhibits significant improvements over existing methods in solving
prediction problems, especially those with large state or parameter
dimensions, and those possessing strongly nonlinear dynamics. Moreover,
our method enables data-driven solution of optimal control problems
involving nonlinear dynamics, with some interesting implications for
controllability.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We present an approach to constructing approximate Koopman-type
decompositions for dynamical systems depending on static or time-varying
parameters. Our method simultaneously constructs an invariant subspace
and a parametric family of projected Koopman operators acting on this
subspace. We parametrize both the projected Koopman operator family and
the dictionary that spans the invariant subspace by neural networks, and
jointly train them with trajectory data. We show theoretically the
validity of our approach and demonstrate via numerical experiments that
it exhibits significant improvements over existing methods in solving
prediction problems, especially those with large state or parameter
dimensions, and those possessing strongly nonlinear dynamics. Moreover,
our method enables data-driven solution of optimal control problems
involving nonlinear dynamics, with some interesting implications for
controllability. - FNClarivate Analytics Web of Science
- VR1.0
- PTJ
- AFYue Guo
Milan Korda
Ioannis G Kevrekidis
Qianxiao Li
- TILearning Parametric Koopman Decompositions for Prediction and Control
- SOSIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
- DTArticle
- ABWe present an approach to constructing approximate Koopman-type
decompositions for dynamical systems depending on static or time-varying
parameters. Our method simultaneously constructs an invariant subspace
and a parametric family of projected Koopman operators acting on this
subspace. We parametrize both the projected Koopman operator family and
the dictionary that spans the invariant subspace by neural networks, and
jointly train them with trajectory data. We show theoretically the
validity of our approach and demonstrate via numerical experiments that
it exhibits significant improvements over existing methods in solving
prediction problems, especially those with large state or parameter
dimensions, and those possessing strongly nonlinear dynamics. Moreover,
our method enables data-driven solution of optimal control problems
involving nonlinear dynamics, with some interesting implications for
controllability. - Z90
- PUSIAM PUBLICATIONS
- PA3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA
- SN1536-0040
- VL24
- BP744
- EP781
- DI10.1137/23M1604576
- UTWOS:001447232500010
- ER
- EF
|
