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Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential equation solver.
A family of embedded Runge–Kutta formulae
Dormand, J. R. and Prince, P. J · 1980
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A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines
Hutchinson, M. F · 1989
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Massaroli, S., Poli, M., Park, J., Yamashita, A., and Asama, H · 2002
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Hypersolvers: Toward Fast Continuous-Depth Models
Massaroli, S., Poli, M., Yamashita, A., Asama, H., and Park, J · 2007
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Adam: A method for stochastic optimization
Kingma, D. and Ba, J · 2015
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A Proposal on Machine Learning via Dynamical Systems
E, W · 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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Neural Ordinary Differential Equations
Chen, R. T. Q., Rubanova, Y., Bettencourt, J., and Duvenaud, D. K · 2018
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Adaptive checkpoint adjoint method for gradient estimation in neural ode
Zhuang, J., Dvornek, N., Li, X., Tatikonda, S., Papademetris, X., and Duncan, J · 2018
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Neural networks with cheap differential operators
Chen, R. T. and Duvenaud, D. K · 2019
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Augmented neural odes
Dupont, E., Doucet, A., and Teh, Y. W · 2019
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Ffjord: Free-form continuous dynamics for scalable reversible generative models
Grathwohl, W., Chen, R. T. Q., Bettencourt, J., Sutskever, I., and Duvenaud, D · 2019
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PyTorch: An Imperative Style, High-Performance Deep Learning Library
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S · 2019
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Diffeqflux.jl-a julia library for neural differential equations
Rackauckas, C., Innes, M., Ma, Y., Bettencourt, J., White, L., and Dixit, V · 2019
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Learning Differential Equations that are Easy to Solve
Kelly, J., Bettencourt, J., Johnson, M. J., and Duvenaud, D · 2020
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torchcde
Kidger, P · 2020
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Neural Controlled Differential Equations for Irregular Time Series
Kidger, P., Morrill, J., Foster, J., and Lyons, T · 2020
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Ot-flow: Fast and accurate continuous normalizing flows via optimal transport
Onken, D., Fung, S. W., Li, X., and Ruthotto, L · 2020
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Snode: Spectral discretization of neural odes for system identification
Quaglino, A., Gallieri, M., Masci, J., and Koutník, J · 2020
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Latent Ordinary Differential Equations for Irregularly-Sampled Time Series
Rubanova, Y., Chen, T. Q., and Duvenaud, D. K · 2019
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How to train your neural ODE: the world of Jacobian and kinetic regularization
Finlay, C., Jacobsen, J.-H., Nurbekyan, L., and Oberman, A. M · 2020
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STEER: Simple Temporal Regularization For Neural ODEs
Ghosh, A., Behl, H. S., Dupont, E., Torr, P. H. S., and Namboodiri, V · 2020
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Warden, P · 2020
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Approximation capabilities of neural odes and invertible residual networks
Zhang, H., Gao, X., Unterman, J., and Arodz, T · 2020
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Symplectic ode-net: Learning hamiltonian dynamics with control
Zhong, Y. D., Dey, B., and Chakraborty, A · 2020
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