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Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed.
On optimal and data-based histograms
D. W. Scott · 1979
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The Fokker-Planck Equation: Methods of Solution and Applications
H. Risken · 1989
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Regression shrinkage and selection via the lasso
R. Tibshirani · 1996
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Moment equations for flow in highly heterogeneous porous media
C. L. Winter, D. M. Tartakovsky, and A. Guadagnini · 2003
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Perspective on theories of anomalous transport in heterogeneous media
S. P. Neuman and D. M. Tartakovsky · 2008
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Distilling free-form natural laws from experimental data
M. Schmidt and H. Lipson · 2009
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Scikit-learn: Machine learning in Python
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay · 2011
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Exact PDF equations and closure approximations for advective-reactive transport
D. Venturi, D. M. Tartakovsky, A. M. Tartakovsky, and G. E. Karniadakis · 2013
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Cumulative distribution function solutions of advection-reaction equations with uncertain parameters
F. Boso, S. V. Broyda, and D. M. Tartakovsky · 2014
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Probabilistic density function method for nonlinear dynamical systems driven by colored noise
D. Barajas-Solano and A. M. Tartakovsky · 2016
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The method of distributions for dispersive transport in porous media with uncertain hydraulic properties
F. Boso and D. M. Tartakovsky · 2016
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
S. L. Brunton, J. L. Proctor, J. N. Kutz, and W. Bialek · 2016
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Learning partial differential equations via data discovery and sparse optimization
H. Schaeffer · 2016
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Method of distributions for uncertainty quantification
D. M. Tartakovsky and P. A. Gremaud · 2016
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Machine learning of linear differential equations using Gaussian processes
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2017
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Data-driven discovery of partial differential equations
S. H. Rudy, S. L. Brunton, J. L. Proctor, and J. N. Kutz · 2017
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Predictive coarse-graining
M. Schöberl, N. Zabaras, and P.-S. Koutsourelakis · 2017
Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks
N. Geneva and N. Zabaras · 2019
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Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks
N. Geneva and N. Zabaras · 2019
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fpinns: Fractional physics-informed neural networks
G. Pang, L. Lu, and G. E. Karniadakis · 2019
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2019
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Data-driven identification of parametric partial differential equations
S. Rudy, A. Alla, S. L. Brunton, and J. N. Kutz · 2019
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Cited alongside, same era.
Method of distributions for water-hammer equations with uncertain parameters
A. Alawadhi, F. Boso, and D. M. Tartakovsky · 2018
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Information-theoretic approach to bidirectional scaling
F. Boso and D. M. Tartakovsky · 2018
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Physics-constrained, data-driven discovery of coarse-grained dynamics
L. Felsberger and P. Koutsourelakis · 2018
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Nonlocal PDF methods for Langevin equations with colored noise
T. Maltba, P. Gremaud, and D. M. Tartakovsky · 2018
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DGM: A deep learning algorithm for solving partial differential equations
J. Sirignano and K. Spiliopoulos · 2018
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Data-informed method of distributions for hyperbolic conservation laws
F. Boso and D. M. Tartakovsky
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Probabilistic forecast of single-phase flow in porous media with uncertain properties
H.-J. Yang, F. Boso, H. A. Tchelepi, and D. M. Tartakovsky · 2019
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Learning on dynamic statistical manifolds
F. Boso and D. M. Tartakovsky · 2020
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Lagrangian dynamic mode decomposition for construction of reduced-order models of advection-dominated phenomena
H. Lu and D. M. Tartakovsky · 2020
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Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems
A. M. Tartakovsky, C. Ortiz Marrero, P. Perdikaris, G. D. Tartakovsky, and D. Barajas-Solano · 2020
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Estimation of distributions via multilevel monte carlo with stratified sampling
S. Taverniers and D. M. Tartakovsky · 2020
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Data-driven deep learning of partial differential equations in modal space
K. Wu and D. Xiu · 2020
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