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Interpretable Nonlinear Dynamic Modeling of Neural Trajectories [article]

Yuan Zhao, Il Memming Park
2016 arXiv   pre-print
We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model assumes low-dimensional continuous dynamics in a finite volume.  ...  of dynamical models and in real neural data.  ...  In this paper, we aim to build an interpretable dynamics model to reverse-engineer the neural implementation of computation.  ... 
arXiv:1608.06546v2 fatcat:vtiwcuvw25ftbcpgtnlvyeqkhe

Variational online learning of neural dynamics [article]

Yuan Zhao, Il Memming Park
2020 arXiv   pre-print
Nonlinear state space models provide an interpretable signal processing framework by combining an intuitive dynamical system with a probabilistic observation model, which can provide insights into neural  ...  Using the stochastic gradient variational Bayes approach, our method jointly optimizes the parameters of the nonlinear dynamical system, the observation model, and the black-box recognition model.  ...  Clinically, a nonlinear state space model provides a basis for nonlinear feedback control as a potential treatment for neurological diseases that arise from diseased dynamical states.  ... 
arXiv:1707.09049v5 fatcat:oq5wq7jwprbd5fiywiu3zbwv74

Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems [article]

Maziar Raissi, Paris Perdikaris, George Em Karniadakis
2018 arXiv   pre-print
In particular, we study the Lorenz system, the fluid flow behind a cylinder, the Hopf bifurcation, and the Glycoltic oscillator model as an example of complicated nonlinear dynamics typical of biological  ...  We test the effectiveness of our approach for several benchmark problems involving the identification of complex, nonlinear and chaotic dynamics, and we demonstrate how this allows us to accurately learn  ...  This comes at the cost of losing interpretability of the learned dynamics.  ... 
arXiv:1801.01236v1 fatcat:rh36qajl6ncdnkga4r5yoxpeli

Data-driven discovery of coordinates and governing equations

Kathleen Champion, Bethany Lusch, J. Nathan Kutz, Steven L. Brunton
2019 Proceedings of the National Academy of Sciences of the United States of America  
The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models.  ...  Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data.  ...  These results demonstrate how to focus neural networks to discover interpretable dynamical models.  ... 
doi:10.1073/pnas.1906995116 pmid:31636218 pmcid:PMC6842598 fatcat:m4swjd6e25b77p6bdpwb2mlgxa

Nonlinear Control in the Nematode C. elegans

Megan Morrison, Charles Fieseler, J. Nathan Kutz
2021 Frontiers in Computational Neuroscience  
We propose a global, nonlinear control model which is minimally parameterized and captures the state transitions described by Markov-switching models with a single dynamical system.  ...  signals in C. elegans neural dynamics can produce switches between stable states.  ...  AUTHOR CONTRIBUTIONS MM was the primary producer of the model with input from CF and JK. The figures for the manuscript were created by MM and the content written by MM, CF, and JK.  ... 
doi:10.3389/fncom.2020.616639 pmid:33551783 pmcid:PMC7862714 fatcat:6o6w6effqzaarbzqaauupjzbge

Learned and Controlled Autonomous Robotic Exploration in an Extreme, Unknown Environment [article]

Frances Zhu, D. Sawyer Elliott, ZhiDi Yang, Haoyuan Zheng
2020 arXiv   pre-print
does not provide an easily interpretable model.  ...  If the models were of interpretable form, designers could use the learned models to inform vehicle and/or control design changes to refine the robot architecture for future applications.  ...  , while providing an interpretable model.  ... 
arXiv:2004.00749v1 fatcat:ydj3vi62z5egjmlubhtyzjt6ie

Neural Network Augmented Physics Models for Systems with Partially Unknown Dynamics: Application to Slider-Crank Mechanism [article]

Wannes De Groote, Edward Kikken, Erik Hostens, Sofie Van Hoecke, Guillaume Crevecoeur
2021 arXiv   pre-print
Dynamic models of mechatronic systems are abundantly used in the context of motion control and design of complex servo applications.  ...  This paper presents a neural network augmented physics (NNAP) model as a combination of physics-inspired and neural layers.  ...  interpretable models.  ... 
arXiv:1910.12212v2 fatcat:tp4euwofczdu5ct2bv4477mevy

Linear dynamical neural population models through nonlinear embeddings [article]

Yuanjun Gao, Evan Archer, Liam Paninski, John P. Cunningham
2016 arXiv   pre-print
Here, we propose fLDS, a general class of nonlinear generative models that permits the firing rate of each neuron to vary as an arbitrary smooth function of a latent, linear dynamical state.  ...  a much larger proportion of neural variability with a small number of latent dimensions, providing superior predictive performance and interpretability.  ...  The GC model can flexibly capture under-and over-dispersed count distributions. 4 Nonlinear latent variable models for neural populations 4.1 Generative Model: Linear dynamical system with nonlinear  ... 
arXiv:1605.08454v2 fatcat:sgn5jdm2dre47gpz55tlx4nqcm

Data-Driven Modeling of Nonlinear Traveling Waves [article]

James Koch
2021 arXiv   pre-print
For these instances, the traveling wave ODEs can be (i) identified in an interpretable manner through an implementation of sparse regression techniques or (ii) modeled empirically with neural ODEs.  ...  Presented is a data-driven Machine Learning (ML) framework for the identification and modeling of traveling wave spatiotemporal dynamics.  ...  Acknowledgements This work was supported by the US Air Force Center of Excellence on Multi-Fidelity Modeling of Rocket Combustor Dynamics award FA9550-17-1-0195.  ... 
arXiv:2101.02122v1 fatcat:oqgsyjmqyffm3f3uqdzd6upxxe

Deep Learning Explicit Differentiable Predictive Control Laws for Buildings [article]

Jan Drgona, Aaron Tuor, Soumya Vasisht, Elliott Skomski, Draguna Vrabie
2021 arXiv   pre-print
Instead, a system dynamics model is learned from the observed system's dynamics, and the neural control law is optimized offline by leveraging the differentiable closed-loop system model.  ...  The control performance of the proposed DPC method is demonstrated in simulation using learned model of multi-zone building thermal dynamics.  ...  The dynamics of control actions u t , and disturbances d t is modeled by nonlinear sub-modules f u , and f d .  ... 
arXiv:2107.11843v1 fatcat:mich22qxp5bchmwv32sdcynr2e

Interpreting Spatial and Temporal Neural Activity Through a Recurrent Neural Network Brain–Machine Interface

J.C. Sanchez, D. Erdogmus, M.A.L. Nicolelis, J. Wessberg, J.C. Principe
2005 IEEE transactions on neural systems and rehabilitation engineering  
In this study, a nonlinear dynamical neural network is trained to predict the hand position of primates from neural recordings in a reaching task paradigm.  ...  We propose the use of optimized brain-machine interface (BMI) models for interpreting the spatial and temporal neural activity generated in motor tasks.  ...  Preliminary studies comparing the reproducibility of this approach through linear and nonlinear models indicated that the interpretations are consistent despite the choice of model [13] .  ... 
doi:10.1109/tnsre.2005.847382 pmid:16003902 fatcat:3mixj3morrf27jworchk7o4yca

Error estimation of recurrent neural network models trained on a finite set of initial values

Binfan Liu, J. Si
1997 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
bounds of state and output trajectories for a class of recurrent neural networks as models of nonlinear dynamic systems.  ...  However, a quantitative evaluation of the performance of nonlinear dynamic neural network models is still lacking.  ...  , matrix inequality, nonlinear H1 control.  ... 
doi:10.1109/81.641775 fatcat:xd4vl3sx3fa3rcmnwxb4v34ame

Data-driven Analysis for Understanding Team Sports Behaviors [article]

Keisuke Fujii
2021 arXiv   pre-print
Although most data-driven models have non-linear structures and high prediction performances, it is sometimes hard to interpret them.  ...  The rules regarding the real-world biological multi-agent behaviors such as team sports are often largely unknown due to their inherently higher-order interactions, cognition, and body dynamics.  ...  For example, learning models with complex nonlinear structures such as neural networks, are actively studied in the field of machine learning.  ... 
arXiv:2102.07545v2 fatcat:hadans3a5nbbzcq4uezz2utj2e

Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling [article]

Kookjin Lee, Nathaniel Trask, Panos Stinis
2021 arXiv   pre-print
We present here a unification of the Sparse Identification of Nonlinear Dynamics (SINDy) formalism with neural ordinary differential equations.  ...  Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability  ...  Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.  ... 
arXiv:2109.05364v1 fatcat:letswnlnxnektob25kr7thq4jm

Deep learning for universal linear embeddings of nonlinear dynamics

Bethany Lusch, J. Nathan Kutz, Steven L. Brunton
2018 Nature Communications  
This work leverages the power of deep learning to discover representations of Koopman eigenfunctions from trajectory data of dynamical systems.  ...  Our network is parsimonious and interpretable by construction, embedding the dynamics on a low-dimensional manifold that is of the intrinsic rank of the dynamics and parameterized by the Koopman eigenfunctions  ...  We would like to thank many people for valuable discussions about neural networks and Koopman theory: Bing Brunton, Karthik Duraisamy, Jean-Christophe Loiseau, Eurika Kaiser, Igor Mezić, Bernd Noack, and  ... 
doi:10.1038/s41467-018-07210-0 pmid:30470743 pmcid:PMC6251871 fatcat:cgsh2i455fblhejlp42vfyqe2m
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