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A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical models of the physical world.
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Automated refinement and inference of analytical models for metabolic networks,
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Predicting catastrophes in nonlinear dynamical systems by compressive sensing,
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Detecting causality in complex ecosystems,
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Nonlinear laplacian spectral analysis for time series with intermittency and low-frequency variability,
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Applied koopmanism a,
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Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling,
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Automatic differentiation in machine learning: a survey,
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems,
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Inferring biological networks by sparse identification of nonlinear dynamics,
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Exact recovery of chaotic systems from highly corrupted data,
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Sparse dynamics for partial differential equations,
H. Schaeffer, R. Caflisch, C. D. Hauck, S. Osher, · 2013
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Compressed modes for variational problems in mathematics and physics,
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A. J. Roberts, Model emergent dynamics in complex systems, SIAM, 2014
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On the compressive spectral method,
A. Mackey, H. Schaeffer, S. Osher, · 2014
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Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems,
S. L. Brunton, J. H. Tu, I. Bright, J. N. Kutz, · 2014
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Exploiting sparsity and equation-free architectures in complex systems,
J. L. Proctor, S. L. Brunton, B. W. Brunton, J. Kutz, · 2014
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Tensorflow: Large-scale machine learning on heterogeneous distributed systems,
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J. N. Kutz, S. L. Brunton, B. W. Brunton, J. L. Proctor, Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, volume 149, SIAM, 2016
2016
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Data-driven discovery of partial differential equations,
S. H. Rudy, S. L. Brunton, J. L. Proctor, J. N. Kutz, · 2017
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Chaos as an intermittently forced linear system,
S. L. Brunton, B. W. Brunton, J. L. Proctor, E. Kaiser, J. N. Kutz, · 2017
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Machine learning of linear differential equations using Gaussian processes,
M. Raissi, P. Perdikaris, G. E. Karniadakis, · 2017
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Hidden physics models: Machine learning of nonlinear partial differential equations,
M. Raissi, G. E. Karniadakis, · 2017
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Multistep neural networks for data-driven discovery of nonlinear dynamical systems,
M. Raissi, P. Perdikaris, G. E. Karniadakis, · 2018
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