Fetching the paper…
Reading the bibliography…
Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics.
E. Hairer and G. Wanner, Solving Ordinary Differential Equations II - Stiff and Differential-Algebraic Problems . Springer, 1991
1991
Earlier work this paper cites.
E. Jones, T. Oliphant, P. Peterson, and others, SciPy: Open source scientific tools for Python , 2001. [Online]. Available: http://www.scipy.org/
2001
Earlier work this paper cites.
L. E. Friberg, A. Henningsson, H. Maas, L. Nguyen, and M. O. Karlsson, “Model of chemotherapy-induced myelosuppression with parameter consistency across drugs,” J Clin Oncol , vol. 20, pp. 4713–21, Dec. 2002
2002
Earlier work this paper cites.
J. D. Murray, Mathematical biology , 3rd ed., ser. Interdisciplinary applied mathematics. New York: Springer, 2002
2002
Earlier work this paper cites.
A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D. E. Shumaker, and C. S. Woodward, “SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers,” ACM Trans. Math. Softw. , vol. 31, pp. 363–396, 2005
2005
Earlier work this paper cites.
C. Kirches, “A Numerical Method for Nonlinear Robust Optimal Control with Implicit Discontinuities and an Application to Powertrain Oscillations,” Ph.D. dissertation, Oct. 2006
2006
Earlier work this paper cites.
M. Peifer and J. Timmer, “Parameter estimation in ordinary differential equations for biochemical processes using the method of multiple shooting,” IET Systems Biology , vol. 1, pp. 78–88, 2007
2007
Earlier work this paper cites.
M. Danhof, E. C. M. de Lange, O. E. Della Pasqua, B. A. Ploeger, and R. A. Voskuyl, “Mechanism-based pharmacokinetic-pharmacodynamic (PK-PD) modeling in translational drug research,” Trends in Pharmacological Sciences , vol. 29, no. 4, pp. 186–191, Apr. 2008. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0165614708000497
2008
Earlier work this paper cites.
K. Soetaert, T. Petzoldt, and R. W. Setzer, “Solving Differential Equations in R: Package deSolve,” Journal of Statistical Software , vol. 33, no. 9, 2010. [Online]. Available: http://www.jstatsoft.org/v33/i09/
2010
Earlier work this paper cites.
F. Hamilton, “Parameter Estimation in Differential Equations: A Numerical Study of Shooting Methods,” SIAM Undergraduate Research Online , vol. 4, pp. 16–31, 2011. [Online]. Available: http://www.siam.org/students/siuro/vol4/S01073.pdf
2011
Earlier work this paper cites.
R. L. Burden and J. D. Faires, Numerical analysis , 9th ed. Boston, MA: Brooks/Cole, Cengage Learning, 2011
2011
Earlier work this paper cites.
B. Steiert, A. Raue, J. Timmer, and C. Kreutz, “Experimental design for parameter estimation of gene regulatory networks,” PLoS ONE , vol. 7, p. e40052, 2012
2012
Cited alongside, same era.
C. Zimmer, “Parameter Estimation for Stochastic Models of Biochemical Reactions,” Journal of Computer Science & Systems Biology , vol. 06, 2013
2013
Cited alongside, same era.
H. T. Banks, D. Robbins, and K. L. Sutton, “Generalized Sensitivity Analysis for Delay Differential Equations,” in Control and Optimization with PDE Constraints , K. Bredies, C. Clason, K. Kunisch, and G. von Winckel, Eds. Basel: Springer Basel, 2013, pp. 19–44
2013
Cited alongside, same era.
2013
Cited alongside, same era.
M. Innes, “Flux: Elegant Machine Learning with Julia,” Journal of Open Source Software , 2018
2018
Closest in time.
2018
Closest in time.
P. K. Mogensen and A. N. Riseth, “Optim: A mathematical optimization package for Julia,” Journal of Open Source Software , vol. 3, no. 24, p. 615, 2018
2018
Closest in time.
J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne, and Q. Zhang, “JAX: composable transformations of Python+NumPy programs,” 2018. [Online]. Available: http://github.com/google/jax
2018
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
H. Zhang and A. Sandu, “FATODE: A Library for Forward, Adjoint, and Tangent Linear Integration of ODEs,” SIAM Journal on Scientific Computing , vol. 36, no. 5, pp. C504–C523, Jan. 2014. [Online]. Available: http://epubs.siam.org/doi/10.1137/130912335
2014
Cited alongside, same era.
2016
Cited alongside, same era.
J. Bezanson, A. Edelman, S. Karpinski, and V. Shah, “Julia: A Fresh Approach to Numerical Computing,” SIAM Review , vol. 59, pp. 65–98, Jan. 2017
2017
Cited alongside, same era.
C. Rackauckas and Q. Nie, “DifferentialEquations.jl - A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia,” Journal of Open Research Software , vol. 5, p. 15, 2017
2017
Cited alongside, same era.
2018
Cited alongside, same era.
2018
Cited alongside, same era.
A. Sommer, “Numerical Methods for Parameter Estimation in Dynamical Systems with Noise,” p. 282
Cited in the paper.
X. Zhen, “Parameter Estimation in Differential Equation Based Models,” Ph.D. dissertation
Cited in the paper.
2018
Closest in time.
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala, “Pytorch: An imperative style, high-performance deep learning library,” in Advances in Neural Information Processing Systems 32 , H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, Eds. Curran Associates, Inc., 2019, pp. 8024–8035. [Online]. Available: http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf
2019
Closest in time.
2019
Closest in time.
C. Rackauckas, A. Edelman, K. Fischer, M. Innes, E. Saba, V. B. Shah, and W. Tebbutt, “Generalized physics-informed learning through language-wide differentiable programming.” 2020
2020
Closest in time.
2020
Closest in time.
W. S. Moses and V. Churavy, “Instead of rewriting foreign code for machine learning, automatically synthesize fast gradients,” in Advances in Neural Information Processing Systems 33 , 2020, to appear in
2020
Closest in time.