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In science we are interested in finding the governing equations, the dynamical rules, underlying empirical phenomena.
Learning Dynamical Systems from Partial Observations
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Learning interpretable continuous-time models of latent stochastic dynamical systems
Duncker, L., Bohner, G., Boussard, J., and Sahani, M · 1902
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EM-like Learning Chaotic Dynamics from Noisy and Partial Observations
Nguyen, D., Ouala, S., Drumetz, L., and Fablet, R · 1903
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Data-driven discovery of coordinates and governing equations
Champion, K., Lusch, B., Kutz, J. N., and Brunton, S. L · 1904
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Identifying nonlinear dynamical systems with multiple time scales and long-range dependencies
Schmidt, D., Koppe, G., Monfared, Z., Beutelspacher, M., and Durstewitz, D · 1910
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Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics
Reinbold, P. A. K., Gurevich, D. R., and Grigoriev, R. O · 1911
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A Dynamically Controlled Recurrent Neural Network for Modeling Dynamical Systems
Fu, Y., Saab Jr, S., Ray, A., and Hauser, M · 1911
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Fantastic Generalization Measures and Where to Find Them, December 2019
Jiang, Y., Neyshabur, B., Mobahi, H., Krishnan, D., and Bengio, S · 1912
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Erzwungene Schwingungen bei veränderlicher Eigenfrequenz und ihre technische Bedeutung
Duffing, G · 1918
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A Contribution to the Mathematical Theory of Epidemics
Kermack, W. O. and McKendrick, A. G · 1927
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Understanding the difficulty of training deep feedforward neural networks
Glorot, X. and Bengio, Y · 1938
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Runge-Kutta neural network for identification of dynamical systems in high accuracy
Wang, Y.-J. and Lin, C.-T · 1941
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Description of stress-strain curves by three parameters, July 1943
Ramberg, W. and Osgood, W. R · 1943
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Deterministic nonperiodic flow
Lorenz, E. N · 1963
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On the Volterra and Other Nonlinear Models of Interacting Populations
Goel, N. S., MAITRA, S. C., and MONTROLL, E. W · 1971
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Ergodic theory of chaos and strange attractors
Eckmann, J. P. and Ruelle, D · 1985
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On the concept of attractor
Milnor, J · 1985
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Predicting chaotic time series
Farmer, J. D. and Sidorowich, J. J · 1987
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Comparison of different methods for computing lyapunov exponents
Geist, K., Parlitz, U., and Lauterborn, W · 1990
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Transverse laser patterns. ii. variational principle for pattern selection, spatial multistability, and laser hydrodynamics
Brambilla, M., Lugiato, L. A., Penna, V., Prati, F., Tamm, C., and Weiss, C. O · 1991
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Differential Equations and Dynamical Systems
Perko, L · 1991
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Approximation of dynamical systems by continuous time recurrent neural networks
Funahashi, K.-i. and Nakamura, Y · 1993
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Controlling chaos in the brain
Schiff, S. J., Jerger, K., Duong, D. H., Chang, T., Spano, M. L., and Ditto, W. L · 1994
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The Limit Cycle of the van der Pol Equation Is Not Algebraic
Odani, K · 1995
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Flat Minima
Hochreiter, S. and Schmidhuber, J · 1997
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Classification of simple low-order models in geophysical fluid dynamics and climate dynamics
Yoden, S · 1997
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Learning dynamical systems by recurrent neural networks from orbits
Kimura, M. and Nakano, R · 1998
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Elements of Applied Bifurcation Theory (2nd Ed.)
Kuznetsov, Y. A · 1998
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Probability distribution characteristics of chaos in a simple population model and the Bonhoeffer–van der Pol oscillator
Parthasarathy, S. and Rajasekar, S · 1998
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Solving inverse problems for odes using the picard contraction mapping
Kunze, H · 1999
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Neurocomputational models of working memory
Durstewitz, D., Seamans, J. K., and Sejnowski, T. J · 2000
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The Nature of Statistical Learning Theory
Vapnik, V. N · 2000
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Deep reconstruction of strange attractors from time series
Gilpin, W · 2002
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Deep Representation Learning for Dynamical Systems Modeling
Shalova, A. and Oseledets, I · 2002
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Forecasting Sequential Data using Consistent Koopman Autoencoders
Azencot, O., Erichson, N. B., Lin, V., and Mahoney, M. W · 2003
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PySINDy: A Python package for the Sparse Identification of Nonlinear Dynamics from Data
de Silva, B. M., Champion, K., Quade, M., Loiseau, J.-C., Kutz, J. N., and Brunton, S. L · 2004
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A new chaotic system and beyond: the generalized lorenz-like system
Lü, J., Chen, G., and Cheng, D · 2004
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Nonlinear dynamical system identification from uncertain and indirect measurements
Voss, H. U., Timmer, J., and Kurths, J · 2004
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Modeling the Kinetics of Bimolecular Reactions
Fernández-Ramos, A., Miller, J. A., Klippenstein, S. J., and Truhlar, D. G · 2006
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Dynamical systems in neuroscience: the geometry of excitability and bursting
Izhikevich, E. M · 2007
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Thresholds and the resilience of caribbean coral reefs
Mumby, P. J., Hastings, A., and Edwards, H. J · 2007
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Strauss, R · 2008
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The Elements of Statistical Learning
Hastie, T., Tibshirani, R., and Friedman, J · 2009
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Optimal transport: old and new , volume 338
Villani, C. et al · 2009
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Nguyen, D., Ouala, S., Drumetz, L., and Fablet, R · 2009
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A theory of learning from different domains
Ben-David, S., Blitzer, J., Crammer, K., Kulesza, A., Pereira, F., and Vaughan, J. W · 2010
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Learnability, Stability and Uniform Convergence
Shalev-Shwartz, S., Shamir, O., Srebro, N., and Sridharan, K · 2010
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Statistical inference for noisy nonlinear ecological dynamic systems
Wood, S. N · 2010
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Extreme multistability in a chemical model system
Ngonghala, C. N., Feudel, U., and Showalter, K · 2011
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Introduction to Smooth Manifolds , volume 218 of Graduate Texts in Mathematics
Lee, J. M · 2012
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Generalization bounds for deep learning, December 2020
Valle-Pérez, G. and Louis, A. A · 2012
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Sliced and radon wasserstein barycenters of measures
Bonneel, N., Rabin, J., Peyré, G., and Pfister, H · 2015
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Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
Brunton, S. L., Proctor, J. L., and Kutz, J. N · 2016
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Complex dynamics and multistability with increasing rationality in market games
Cavalli, F. and Naimzada, A · 2016
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Sliced Wasserstein Kernels for Probability Distributions
Kolouri, S., Zou, Y., and Rohde, G. K · 2016
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Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
Brunton, S. L., Proctor, J. L., and Kutz, J. N · 2016
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Recurrent switching linear dynamical systems, October 2016
Linderman, S. W., Miller, A. C., Adams, R. P., Blei, D. M., Paninski, L., and Johnson, M. J · 2016
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LFADS - Latent Factor Analysis via Dynamical Systems
Sussillo, D., Jozefowicz, R., Abbott, L. F., and Pandarinath, C · 2016
Cited alongside, same era.
Synthesis of recurrent neural networks for dynamical system simulation
Robust forecasting using predictive generalized synchronization in reservoir computing
Platt, J. A., Wong, A., Clark, R., Penny, S. G., and Abarbanel, H. D · 2021
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Learn to synchronize, synchronize to learn
Verzelli, P., Alippi, C., and Livi, L · 2021
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A diffusion theory for deep learning dynamics: Stochastic gradient descent exponentially favors flat minima
Xie, Z., Sato, I., and Sugiyama, M · 2021
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Transformers for modeling physical systems
Geneva, N. and Zabaras, N · 2021
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Goyal, P. and Benner, P · 2021
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Learning Dynamical Systems from Noisy Sensor Measurements using Multiple Shooting
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Trischler, A. and D’Eleuterio, G. M · 2016
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The Geometric Approach for Constructing Sinai–Ruelle–Bowen Measures
Climenhaga, V., Luzzatto, S., and Pesin, Y · 2017
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Sharp Minima Can Generalize For Deep Nets
Dinh, L., Pascanu, R., Bengio, S., and Bengio, Y · 2017
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Advanced Data Analysis in Neuroscience
Durstewitz, D · 2017
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Constrained sparse Galerkin regression
Loiseau, J.-C. and Brunton, S. L · 2017
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Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data
Pathak, J., Lu, Z., Hunt, B. R., Girvan, M., and Ott, E · 2017
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DifferentialEquations.jl–a performant and feature-rich ecosystem for solving differential equations in Julia
Rackauckas, C. and Nie, Q · 2017
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Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks
Vlachas, P. R., Byeon, W., Wan, Z. Y., Sapsis, T. P., and Koumoutsakos, P · 2017
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Jordana, A., Carpentier, J., and Righetti, L · 2021
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Inferring Latent Dynamics Underlying Neural Population Activity via Neural Differential Equations
Kim, T. D., Luo, T. Z., Pillow, J. W., and Brody, C · 2021
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A unified and automated approach to attractor reconstruction
Kraemer, K. H., Datseris, G., Kurths, J., Kiss, I. Z., Ocampo-Espindola, J. L., and Marwan, N · 2021
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Structural identification with physics-informed neural ordinary differential equations
Lai, Z., Mylonas, C., Nagarajaiah, S., and Chatzi, E · 2021
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Liu, Z. and Jin, L · 2021
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Lu, L., Jin, P., Pang, G., Zhang, Z., and Karniadakis, G. E · 2021
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Neural Dynamical Systems: Balancing Structure and Flexibility in Physical Prediction
Mehta, V., Char, I., Neiswanger, W., Chung, Y., Nelson, A., Boyer, M., Kolemen, E., and Schneider, J · 2021
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Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systems
Schlaginhaufen, A., Wenk, P., Krause, A., and Dörfler, F · 2021
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Dynamical time series embeddings in recurrent neural networks
Uribarri, G. and Mindlin, G. B · 2021
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Continual Learning of Dynamical Systems With Competitive Federated Reservoir Computing
Bereska, L. and Gavves, E · 2022
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Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems
Brenner, M., Hess, F., Mikhaeil, J. M., Bereska, L. F., Monfared, Z., Kuo, P.-C., and Durstewitz, D · 2022
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Automatic differentiation to simultaneously identify nonlinear dynamics and extract noise probability distributions from data
Kaheman, K., Brunton, S. L., and Kutz, J. N · 2022
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Attractor and integrator networks in the brain
Khona, M. and Fiete, I. R · 2022
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Generalizing to New Physical Systems via Context-Informed Dynamics Model, June 2022
Kirchmeyer, M., Yin, Y., Donà, J., Baskiotis, N., Rakotomamonjy, A., and Gallinari, P · 2022
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On the difficulty of learning chaotic dynamics with RNNs
Mikhaeil, J. M., Monfared, Z., and Durstewitz, D · 2022
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Patel, D. and Ott, E · 2022
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Platt, J. A., Penny, S. G., Smith, T. A., Chen, T.-C., and Abarbanel, H. D. I · 2022
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Probabilistic physics-informed machine learning for dynamic systems
Subramanian, A. and Mahadevan, S · 2022
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Multiscale simulations of complex systems by learning their effective dynamics
Vlachas, P. R., Arampatzis, G., Uhler, C., and Koumoutsakos, P · 2022
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On lyapunov exponents for RNNs: Understanding information propagation using dynamical systems tools
Vogt, R., Puelma Touzel, M., Shlizerman, E., and Lajoie, G · 2022
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Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems
Brenner, M., Hess, F., Mikhaeil, J. M., Bereska, L. F., Monfared, Z., Kuo, P.-C., and Durstewitz, D · 2022
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Chaos as an interpretable benchmark for forecasting and data-driven modelling
Gilpin, W · 2022
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Stabilized neural ordinary differential equations for long-time forecasting of dynamical systems
Linot, A. J., Burby, J. W., Tang, Q., Balaprakash, P., Graham, M. D., and Maulik, R · 2022
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On the difficulty of learning chaotic dynamics with RNNs
Mikhaeil, J. M., Monfared, Z., and Durstewitz, D · 2022
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Long Expressive Memory for Sequence Modeling
Rusch, T. K., Mishra, S., Erichson, N. B., and Mahoney, M. W · 2022
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A sparse Bayesian framework for discovering interpretable nonlinear stochastic dynamical systems with Gaussian white noise
Tripura, T. and Chakraborty, S · 2022
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LEADS: Learning Dynamical Systems that Generalize Across Environments, February 2022
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Learning chaotic systems from noisy data via multi-step optimization and adaptive training
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Simplicity bias in transformers and their ability to learn sparse boolean functions, 2023
Bhattamishra, S., Patel, A., Kanade, V., and Blunsom, P · 2023
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Odeformer: Symbolic regression of dynamical systems with transformers
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Is Out-of-Distribution Detection Learnable?, February 2023
Fang, Z., Li, Y., Lu, J., Dong, J., Han, B., and Liu, F · 2023
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Disentangled Generative Models for Robust Prediction of System Dynamics
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Generalized Teacher Forcing for Learning Chaotic Dynamics
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Training neural operators to preserve invariant measures of chaotic attractors, 2023
Jiang, R., Lu, P. Y., Orlova, E., and Willett, R · 2023
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Homotopy-based training of NeuralODEs for accurate dynamics discovery, May 2023
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Do deep neural networks have an inbuilt occam’s razor?, 2023
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MetaPhysiCa: OOD Robustness in Physics-informed Machine Learning, March 2023
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Generalized Teacher Forcing for Learning Chaotic Dynamics
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Same occupation measure → \rightarrow same trajectory
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