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Integrating physics models within machine learning models holds considerable promise toward learning robust models with improved interpretability and abilities to extrapolate.
A hybrid neural network-first principles approach to process modeling
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Continuous-time nonlinear signal processing: A neural network based approach for gray box identification
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Latent force models
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Thermodynamic consistent neural networks for learning material interfacial mechanics
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Bayesian Data Analysis
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Auto-encoding variational Bayes
D. P. Kingma and M. Welling · 2014
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Stochastic backpropagation and approximate inference in deep generative models
D. J. Rezende, S. Mohamed, and D. Wierstra · 2014
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Research Methods in Biomechanics
D. G. E. Robertson, G. E. Caldwell, J. Hamill, G. Kamen, and S. N. Whittlesey · 2014
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A recurrent latent variable model for sequential data
J. Chung, K. Kastner, L. Dinh, K. Goel, A. Courville, and Y. Bengio · 2015
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Imfit: A fast, flexible new program for astronomical image fitting
P. Erwin · 2015
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Sequential neural models with stochastic layers
M. Fraccaro, S. K. Sønderby, U. Paquet, and O. Winther · 2016
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OptNet: Differentiable optimization as a layer in neural networks
B. Amos and J. Z. Kolter · 2017
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β \beta -VAE: Learning basic visual concepts with a constrained variational framework
I. Higgins, L. Matthey, A. Pal, C. Burgess, X. Glorot, M. Botvinick, S. Mohamed, and A. Lerchner · 2017
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Deep variational Bayes filters: Unsupervised learning of state space models from raw data
M. Karl, M. Soelch, J. Bayer, and P. van der Smagt · 2017
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Structured inference networks for nonlinear state space models
R. G. Krishnan, U. Shalit, and D. Sontag · 2017
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Hybrid analytical and data-driven modeling for feed-forward robot control
R. Reinhart, Z. Shareef, and J. Steil · 2017
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Label-free supervision of neural networks with physics and domain knowledge
R. Stewart and S. Ermon · 2017
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A physically based and machine learning hybrid approach for accurate rainfall-runoff modeling during extreme typhoon events
C.-C. Young, W.-C. Liu, and M.-C. Wu · 2017
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Augmenting physical simulators with stochastic neural networks: Case study of planar pushing and bouncing
A. Ajay, J. Wu, N. Fazeli, M. Bauza, L. P. Kaelbling, J. B. Tenenbaum, and A. Rodriguez · 2018
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Gaussian process prior variational autoencoders
F. P. Casale, A. Dalca, L. Saglietti, J. Listgarten, and N. Fusi · 2018
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PGA: Physics guided and adaptive approach for mobile fine-grained air pollution estimation
X. Chen, X. Xu, X. Liu, S. Pan, J. He, H. Y. Noh, L. Zhang, and P. Zhang · 2018
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Sim-to-real transfer with neural-augmented robot simulation
F. Golemo, P.-Y. Oudeyer, A. A. Taïga, and A. Courville · 2018
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Data-augmented contact model for rigid body simulation
Y. Jiang, J. Sun, and C. K. Liu · 2018
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Deep learning of multi-element abundances from high-resolution spectroscopic data
H. W. Leung and J. Bovy · 2018
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Disentangled sequential autoencoder
Y. Li and S. Mandt · 2018
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HybridNet: Integrating model-based and data-driven learning to predict evolution of dynamical systems
Y. Long and X. She · 2018
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PDE-net: Learning PDEs from data
Z. Long, Y. Lu, X. Ma, and B. Dong · 2018
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Data-driven Urban Energy Simulation (DUE-S): A framework for integrating engineering simulation and machine learning methods in a multi-scale urban energy modeling workflow
A. Nutkiewicz, Z. Yang, and R. K. Jain · 2018
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Deep hidden physics models: Deep learning of nonlinear partial differential equations
M. Raissi · 2018
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Learning with weak supervision from physics and data-driven constraints
H. Ren, R. Stewart, J. Song, V. Kuleshov, and S. Ermon · 2018
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Data-assisted reduced-order modeling of extreme events in complex dynamical systems
Z. Y. Wan, P. Vlachas, P. Koumoutsakos, and T. Sapsis · 2018
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Physics-informed deep generative models
Y. Yang and P. Perdikaris · 2018
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The information autoencoding family: A Lagrangian perspective on latent variable generative models
S. Zhao, J. Song, and S. Ermon · 2018
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Combining physical simulators and object-based networks for control
A. Ajay, M. Bauza, J. Wu, N. Fazeli, J. B. Tenenbaum, A. Rodriguez, and L. P. Kaelbling · 2019
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Blending diverse physical priors with neural networks
Y. Ba, G. Zhao, and A. Kadambi · 2019
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Deep learning for physical processes: Incorporating prior scientific knowledge
E. de Bézenac, A. Pajot, and P. Gallinari · 2019
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W. De Groote, E. Kikken, E. Hostens, S. Van Hoecke, and G. Crevecoeur · 2019
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Hamiltonian neural networks
S. Greydanus, M. Dzamba, and J. Yosinski · 2019
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Physics guided RNNs for modeling dynamical systems: A case study in simulating lake temperature profiles
X. Jia, J. Willard, A. Karpatne, J. Read, J. Zwart, M. Steinbach, and V. Kumar · 2019
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PhyNet: Physics guided neural networks for particle drag force prediction in assembly
N. Muralidhar, J. Bu, Z. Cao, L. He, N. Ramakrishnan, D. Tafti, and A. Karpatne · 2020
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Solving inverse-PDE problems with physics-aware neural networks
S. Pakravan, P. A. Mistani, M. A. Aragon-Calvo, and F. Gibou · 2020
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Physics guided machine learning using simplified theories
S. Pawar, O. San, B. Aksoylu, A. Rasheed, and T. Kvamsdal · 2020
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Universal differential equations for scientific machine learning
C. Rackauckas, Y. Ma, J. Martensen, C. Warner, K. Zubov, R. Supekar, D. Skinner, A. Ramadhan, and A. Edelman · 2020
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Hybrid physical-deep learning model for astronomical inverse problems
F. Lanusse, P. Melchior, and F. Moolekamp · 2019
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Human kinematic, kinetic and EMG data during different walking and stair ascending and descending tasks
T. Lencioni, I. Carpinella, M. Rabuffetti, A. Marzegan, and M. Ferrarin · 2019
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PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network
Z. Long, Y. Lu, and B. Dong · 2019
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Deep Lagrangian networks: Using physics as model prior for deep learning
M. Lutter, C. Ritter, and J. Peters · 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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Deep learning and process understanding for data-driven Earth system science
M. Reichstein, G. Camps-Valls, B. Stevens, M. Jung, J. Denzler, N. Carvalhais, and Prabhat · 2019
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PI-LSTM: Physics-infused long short-term memory metwork
S. K. Singh, R. Yang, A. Behjat, R. Rai, S. Chowdhury, and I. Matei · 2019
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M. Rixner and P.-S. Koutsourelakis · 2020
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Modeling system dynamics with physics-informed neural networks based on Lagrangian mechanics
M. A. Roehrl, T. A. Runkler, V. Brandtstetter, M. Tokic, and S. Obermayer · 2020
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Variational integrator networks for physically structured embeddings
S. Saemundsson, A. Terenin, K. Hofmann, and M. Deisenroth · 2020
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Ensembling geophysical models with Bayesian neural networks
U. Sengupta, M. Amos, J. S. Hosking, C. E. Rasmussen, M. Juniper, and P. J. Young · 2020
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N. Shlezinger, J. Whang, Y. C. Eldar, and A. G. Dimakis · 2020
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Variational autoencoding of PDE inverse problems
D. J. Tait and T. Damoulas · 2020
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Hamiltonian generative networks
P. Toth, D. J. Rezende, A. Jaegle, S. Racanière, A. Botev, and I. Higgins · 2020
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Solver-in-the-Loop: Learning from differentiable physics to interact with iterative PDE-Solvers
K. Um, R. Brand, Y. R. Fei, P. Holl, and N. Therey · 2020
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Informed machine learning – A taxonomy and survey of integrating knowledge into learning systems
L. von Rueden, S. Mayer, K. Beckh, B. Georgiev, S. Giesselbach, R. Heese, B. Kirsch, J. Pfrommer, A. Pick, R. Ramamurthy, M. Walczak, J. Garcke, C. Bauckhage, and J. Schuecker · 2020
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Combining machine learning and simulation to a hybrid modelling approach: Current and future directions
L. von Rueden, S. Mayer, R. Sifa, C. Bauckhage, and J. Garcke · 2020
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Integrating physics-based modeling with machine learning: A survey
J. Willard, X. Jia, S. Xu, M. Steinbach, and V. Kumar · 2020
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Explainable machine learning with prior knowledge: An overview
K. Beckh, S. Müller, M. Jakobs, V. Toborek, H. Tan, R. Fischer, P. Welke, S. Houben, and L. von Rueden · 2021
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Neural networks with physics-informed architectures and constraints for dynamical systems modeling
F. Djeumou, C. Neary, E. Goubault, S. Putot, and U. Topcu · 2021
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Variational data assimilation with a learned inverse observation operator
T. Frerix, D. Kochkov, J. A. Smith, D. Cremers, M. P. Brenner, and S. Hoyer · 2021
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SimGAN: Hybrid simulator identification for domain adaptation via adversarial reinforcement learning
Y. Jiang, T. Zhang, D. Ho, Y. Bai, C. K. Liu, S. Levine, and J. Tan · 2021
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Physics-aware, probabilistic model order reduction with guaranteed stability
S. Kaltenbach and P.-S. Koutsourelakis · 2021
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Physics-informed machine learning
G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang · 2021
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AdjointNet: Constraining machine learning models with physics-based codes
S. Karra, B. Ahmmed, and M. K. Mudunuru · 2021
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Structured representation learning using structural autoencoders and hybridization
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Hybrid FEM-NN models: Combining artificial neural networks with the finite element method
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Model-constrained deep learning approaches for inverse problems
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Grey-box models for wave loading prediction
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Integrating expert ODEs into Neural ODEs: Pharmacology and disease progression
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Towards causal representation learning
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Amortized synthesis of constrained configurations using a differentiable surrogate
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Estimating model inadequacy in ordinary differential equations with physics-informed neural networks
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Understanding and mitigating gradient flow pathologies in physics-informed neural networks
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B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
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Augmenting physical models with deep networks for complex dynamics forecasting
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MIDPhyNet: Memorized infusion of decomposed physics in neural networks to model dynamic systems
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