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In the area of physical simulations, nearly all neural-network-based methods directly predict future states from the input states.
Interactive dynamics
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Fast contact force computation for nonpenetrating rigid bodies
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Impulse-based simulation of rigid bodies
Mirtich, B. and Canny, J · 1995
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Smoothed particle hydrodynamics
Monaghan, J · 2005
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Numerical Optimization
Nocedal, J. and Wright, S. J · 2006
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Efficient simulation of inextensible cloth
Goldenthal, R., Harmon, D., Fattal, R., Bercovier, M., and Grinspun, E · 2007
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Position based dynamics
Müller, M., Heidelberger, B., Hennix, M., and Ratcliff, J · 2007
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Continuum-based strain limiting
Thomaszewski, B., Pabst, S., and Strasser, W · 2009
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Mujoco: A physics engine for model-based control
Todorov, E., Erez, T., and Tassa, Y · 2012
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Projective dynamics: Fusing constraint projections for fast simulation
Bouaziz, S., Martin, S., Liu, T., Kavan, L., and Pauly, M · 2014
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Layer normalization, 2016
Ba, J. L., Kiros, J. R., and Hinton, G. E · 2016
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Interaction networks for learning about objects, relations and physics
Battaglia, P., Pascanu, R., Lai, M., Rezende, D. J., and Kavukcuoglu, K · 2016
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Optnet: Differentiable optimization as a layer in neural networks
Amos, B. and Kolter, J. Z · 2017
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Geometric deep learning: going beyond euclidean data
Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., and Vandergheynst, P · 2017
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Relational inductive biases, deep learning, and graph networks
Battaglia, P. W., Hamrick, J. B., Bapst, V., Sanchez-Gonzalez, A., Zambaldi, V., Malinowski, M., Tacchetti, A., Raposo, D., Santoro, A., Faulkner, R., et al · 2018
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Neural ordinary differential equations
Chen, R. T., Rubanova, Y., Bettencourt, J., and Duvenaud, D · 2018
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Reviving and improving recurrent back-propagation
Liao, R., Xiong, Y., Fetaya, E., Zhang, L., Yoon, K., Pitkow, X., Urtasun, R., and Zemel, R. S · 2018
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Flexible neural representation for physics prediction
Mrowca, D., Zhuang, C., Wang, E., Haber, N., Fei-Fei, L., Tenenbaum, J. B., and Yamins, D. L · 2018
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Graph networks as learnable physics engines for inference and control
Sanchez-Gonzalez, A., Heess, N., Springenberg, J. T., Merel, J., Riedmiller, M., Hadsell, R., and Battaglia, P · 2018
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Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework
Wu, J.-L., Xiao, H., and Paterson, E · 2018
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Continuous latent search for combinatorial optimization
Bartunov, S., Nair, V., Battaglia, P., and Lillicrap, T · 2020
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Cranmer, M., Greydanus, S., Hoyer, S., Battaglia, P., Spergel, D., and Ho, S · 2020
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Combining differentiable PDE solvers and graph neural networks for fluid flow prediction
De Avila Belbute-Peres, F., Economon, T., and Kolter, Z · 2020
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Deep implicit layers - neural odes, deep equilibrium models, and beyond, 2020
Duvenaud, D., Kolter, Z., and Johnson, M · 2020
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Simplifying hamiltonian and lagrangian neural networks via explicit constraints
Finzi, M., Wang, K. A., and Wilson, A. G · 2020
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Application of convolutional neural network to predict airfoil lift coefficient
Zhang, Y., Sung, W. J., and Mavris, D. N · 2018
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Bai, S., Kolter, J. Z., and Koltun, V · 2019
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Symplectic recurrent neural networks
Chen, Z., Zhang, J., Arjovsky, M., and Bottou, L · 2019
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Hamiltonian neural networks
Greydanus, S., Dzamba, M., and Yosinski, J · 2019
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Learning particle dynamics for manipulating rigid bodies, deformable objects, and fluids
Li, Y., Wu, J., Tedrake, R., Tenenbaum, J. B., and Torralba, A · 2019
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Deep lagrangian networks: Using physics as model prior for deep learning
Lutter, M., Ritter, C., and Peters, J · 2019
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Latent odes for irregularly-sampled time series
Rubanova, Y., Chen, R. T., and Duvenaud, D · 2019
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Learning constraint-based planning models from demonstrations
Loula, J., Allen, K., Silver, T., and Tenenbaum, J · 2020
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Learning to simulate complex physics with graph networks
Sanchez-Gonzalez, A., Godwin, J., Pfaff, T., Ying, R., Leskovec, J., and Battaglia, P · 2020
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Deep learning methods for reynolds-averaged navier–stokes simulations of airfoil flows
Thuerey, N., Weißenow, K., Prantl, L., and Hu, X · 2020
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Scipy 1.0: fundamental algorithms for scientific computing in python
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., et al · 2020
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Learning physical constraints with neural projections
Yang, S., He, X., and Zhu, B · 2020
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Dc3: A learning method for optimization with hard constraints
Donti, P. L., Rolnick, D., and Kolter, J. Z · 2021
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Physics-informed machine learning
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., and Yang, L · 2021
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Machine learning–accelerated computational fluid dynamics
Kochkov, D., Smith, J. A., Alieva, A., Wang, Q., Brenner, M. P., and Hoyer, S · 2021
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Learning mesh-based simulation with graph networks
Pfaff, T., Fortunato, M., Sanchez-Gonzalez, A., and Battaglia, P · 2021
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Learned coarse models for efficient turbulence simulation
Stachenfeld, K., Fielding, D. B., Kochkov, D., Cranmer, M., Pfaff, T., Godwin, J., Cui, C., Ho, S., Battaglia, P., and Sanchez-Gonzalez, A · 2021
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