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Democratization of machine learning requires architectures that automatically adapt to new problems.
Beitrag zur naherungsweisen integration totaler differentialgleichungen
Kutta, W · 1901
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Diffeqflux.jl - A julia library for neural differential equations
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Classical fifth-, sixth-, seventh-, and eighth-order Runge-Kutta formulas with stepsize control
Fehlberg, E · 1968
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Stiffness and nonstiff differential equation solvers, ii: Detecting stiffness with runge-kutta methods
Shampine, L. F · 1977
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Shampine, L. F. and Gear, C. W · 1979
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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
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Solving Ordinary Differential Equations I: Nonstiff Problems , volume 8
Hairer, E., Norsett, S., and Wanner, G · 1993
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Stiffness of odes
Higham, D. J. and Trefethen, L. N · 1993
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Solving ordinary differential equations II
Wanner, G. and Hairer, E · 1996
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Computer methods for ordinary differential equations and differential-algebraic equations , volume 61
Ascher, U. M. and Petzold, L. R · 1998
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Iterative methods for optimization
Kelley, C. T · 1999
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On the momentum term in gradient descent learning algorithms
Qian, N · 1999
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The data-flow equations of checkpointing in reverse automatic differentiation
Dauvergne, B. and Hascoët, L · 2006
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Estimation of the parameters of stochastic differential equations
Jeisman, J. I · 2006
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Stiff systems
Shampine, L. F. and Thompson, S · 2007
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Computing the high order derivatives with automatic differentiation and its application in chebyshev’s method
Zhang, H., Xue, Y., Zhang, C., and Dong, L · 2008
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Runge–kutta pairs of order 5(4) satisfying only the first column simplifying assumption
Tsitouras, C · 2011
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Predicting in-hospital mortality of icu patients: The physionet/computing in cardiology challenge 2012
Silva, I., Moody, G., Scott, D. J., Celi, L. A., and Mark, R. G · 2012
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Fatode: a library for forward, adjoint, and tangent linear integration of odes
Zhang, H. and Sandu, A · 2014
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Deep residual learning for image recognition, 2015
He, K., Zhang, X., Ren, S., and Sun, J · 2015
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Adam: A method for stochastic optimization, 2014
Kingma, D. P. and Ba, J · 2015
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Generalized method of moments for estimating parameters of stochastic reaction networks
Bai, S., Kolter, J. Z., and Koltun, V · 2019
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Taylor-mode automatic differentiation for higher-order derivatives in jax
Bettencourt, J., Johnson, M. J., and Duvenaud, D · 2019
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Anode: Unconditionally accurate memory-efficient gradients for neural odes
Gholami, A., Keutzer, K., and Biros, G · 2019
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Neural sde: Stabilizing neural ode networks with stochastic noise, 2019
Liu, X., Xiao, T., Si, S., Cao, Q., Kumar, S., and Hsieh, C.-J · 2019
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Confederated modular differential equation apis for accelerated algorithm development and benchmarking
Rackauckas, C. and Nie, Q · 2019
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Lück, A. and Wolf, V · 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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Julia: A fresh approach to numerical computing
Bezanson, J., Edelman, A., Karpinski, S., and Shah, V. B · 2017
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Adaptive methods for stochastic differential equations via natural embeddings and rejection sampling with memory
Rackauckas, C. and Nie, Q · 2017
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Neural ordinary differential equations
Chen, R. T., Rubanova, Y., Bettencourt, J., and Duvenaud, D. K · 2018
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Ffjord: Free-form continuous dynamics for scalable reversible generative models
Grathwohl, W., Chen, R. T., Bettencourt, J., Sutskever, I., and Duvenaud, D · 2018
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Don’t unroll adjoint: Differentiating ssa-form programs
Innes, M · 2018
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Rubanova, Y., Chen, R. T., and Duvenaud, D · 2019
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Steer: simple temporal regularization for neural odes
Behl, H., Ghosh, A., Dupont, E., Torr, P., and Namboodiri, V · 2020
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Finlay, C., Jacobsen, J.-H., Nurbekyan, L., and Oberman, A. M · 2020
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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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”hey, that’s not an ode”: Faster ode adjoints with 12 lines of code, 2020
Kidger, P., Chen, R. T. Q., and Lyons, T · 2020
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Onken, D. and Ruthotto, L · 2020
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Hypersolvers: Toward fast continuous-depth models
Poli, M., Massaroli, S., Yamashita, A., Asama, H., and Park, J · 2020
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Stability-optimized high order methods and stiffness detection for pathwise stiff stochastic differential equations
Rackauckas, C. and Nie, Q · 2020
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Deep euler method: solving odes by approximating the local truncation error of the euler method
Shen, X., Cheng, X., and Liang, K · 2020
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Adabelief optimizer: Adapting stepsizes by the belief in observed gradients
Zhuang, J., Tang, T., Ding, Y., Tatikonda, S., Dvornek, N., Papademetris, X., and Duncan, J · 2020
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{MALI}: A memory efficient and reverse accurate integrator for neural {ode}s
Zhuang, J., Dvornek, N. C., sekhar tatikonda, and s Duncan, J · 2021
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