A generalized framework for microstructural optimization using neural networks by Saketh Sridhara, Aaditya Chandrasekhar, Krishnan Suresh

“…The framework relies on the classic density formulation of microstructural optimization, but the density field is represented through the NN’s weights and biases.The main characteristics of the proposed NN framework are: (1) it supports automatic differentiation, eliminating the need for manual sensitivity derivations, (2) smoothing filters are not required due to implicit filtering, (3) the framework can be easily extended to multiple-materials, and (4) a high-resolution microstructural topology can be recovered through a simple post-processing step. …”
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JAXVacua — a framework for sampling string vacua by A. Dubey, S. Krippendorf, A. Schachner

“…In this paper, we implement algorithms based on JAX, heavily utilising automatic differentiation, just-in-time compilation and parallelisation features, to efficiently construct string vacua. …”
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Inversion of a Stokes glacier flow model emulated by deep learning by Guillaume Jouvet

“…By substituting the ice flow equations using a convolutional neural network emulator, we simplify, make more robust and dramatically speed up the solving of the underlying optimization problem thanks to automatic differentiation, stochastic gradient methods and implementation of graphics processing unit (GPU). …”
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Physics-Based Differentiable Rendering for Efficient and Plausible Fluid Modeling from Monocular Video by Yunchi Cen, Qifan Zhang, Xiaohui Liang

“…Rather than relying on automatic differentiation, we derive the differential form of the radiance transfer equation under single scattering. …”
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Sensitivity computation of statistically stationary quantities in turbulent flows by Chandramoorthy, Nisha, Wang, Qiqi

“…It is well-known that linearized perturbation methods for sensitivity analysis, such as tangent or adjoint equation-based, finite difference and automatic differentiation are not suitable for turbulent flows. …”
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Optim: A mathematical optimization package for Julia by Mogensen, P, Riseth, A

“…The user can provide derivatives themselves, or request that they are calculated using automatic differentiation or finite difference methods. The main focus of the package has currently been on unconstrained optimization, however, box-constrained optimization is supported, and a more comprehensive support for constraints is underway. …”

Small steps and giant leaps: minimal newton solvers for deep learning by Henriques, J, Ehrhardt, S, Albanie, S, Vedaldi, A

“…Compared to stochastic gradient descent (SGD), it only requires two additional forward-mode automatic differentiation operations per iteration, which has a computational cost comparable to two standard forward passes and is easy to implement. …”

Curve Fitting Algorithm of Functional Radiation-Response Data Using Bayesian Hierarchical Gaussian Process Regression Model by Kwang-Woo Jung, Jaeoh Kim, Ho-Jin Jung, Seung-Won Seo, Ji-Man Hong, Hyoung-Woo Bai, Seongil Jo

“…The NBH model is based on a Bayesian hierarchical (BH) model with a Gaussian-Inverse Wishart process (G-IWP) prior, which simultaneously smooths multiple functional observations and estimates mean-covariance functions. We use the automatic differentiation variational inference (ADVI) algorithm with a Gaussian distribution as the variational distribution for approximating the posterior distribution of parameters of interest, which is applicable to a wide class of probabilistic models and can also be implemented in Stan (a probabilistic programming system). …”
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Optimal control of large quantum systems: assessing memory and runtime performance of GRAPE by Yunwei Lu, Sandeep Joshi, Vinh San Dinh, Jens Koch

“…Gradient Ascent Pulse Engineering (GRAPE) is a popular technique in quantum optimal control, and can be combined with automatic differentiation (AD) to facilitate on-the-fly evaluation of cost-function gradients. …”
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Systematically differentiating parametric discontinuities by Bangaru, Sai Praveen, Michel, Jesse, Mu, Kevin, Bernstein, Gilbert, Li, Tzu-Mao, Ragan-Kelley, Jonathan

“…Previous approaches either apply specialized hand-derived solutions, smooth out the discontinuities, or rely on incorrect automatic differentiation.</jats:p> <jats:p>We propose a systematic approach to differentiating integrals with discontinuous integrands, by developing a new differentiable programming language. …”
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Optimization of a dual mixed refrigerant process using a nonsmooth approach by Vikse, Matias, Watson, Harry AJ, Kim, Donghoi, Barton, Paul I, Gundersen, Truls

“…New improved operating conditions are obtained using the primal-dual interior-point optimizer IPOPT, with sensitivity information calculated using new developments in nonsmooth analysis to obtain generalized derivative information using a nonsmooth generalization of the vector forward mode of automatic differentiation. Several optimization studies are performed with constraints on both the minimum temperature difference (ΔTmin) and total heat exchanger conductance (UAmax) used to represent the trade-offs between energy consumption and the required heat transfer area. …”
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Differentiable sampling of molecular geometries with uncertainty-based adversarial attacks by Schwalbe-Koda, Daniel, Tan, Aik Rui, Gómez-Bombarelli, Rafael

“…Here, we exploit automatic differentiation to drive atomistic systems towards high-likelihood, high-uncertainty configurations without the need for molecular dynamics simulations. …”
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Getting to the point: index sets and parallelism-preserving autodiff for pointful array programming by Paszke, Adam, Johnson, Daniel D, Duvenaud, David, Vytiniotis, Dimitrios, Radul, Alexey, Johnson, Matthew J, Ragan-Kelley, Jonathan, Maclaurin, Dougal

“…Specifically, an associative accumulation effect allows reverse-mode automatic differentiation of in-place updates in a way that preserves parallelism. …”
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SedTrace 1.0: a Julia-based framework for generating and running reactive-transport models of marine sediment diagenesis specializing in trace elements and isotopes by J. Du

“…The resulting code is clearly structured and readable, and it is integrated with Julia's differential equation solving ecosystems, utilizing tools such as automatic differentiation, sparse numerical methods, Newton–Krylov solvers and preconditioners. …”
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On the Development of an Implicit Discontinuous Galerkin Solver for Turbulent Real Gas Flows by Edoardo Mantecca, Alessandro Colombo, Antonio Ghidoni, Gianmaria Noventa, David Pasquale, Stefano Rebay

“…An implicit time integration is adopted; Jacobian matrix and thermodynamic derivatives are obtained with the automatic differentiation tool Tapenade. The solver accuracy is assessed by computing both steady and unsteady real gas test cases available in the literature, and the effect of the mesh size and polynomial degree of approximation on the solution accuracy is investigated. …”
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Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework by Birkisson, A

“…In this work, we present how automatic differentiation techniques can be applied to compute Fréchet derivatives. …”

Korg: A Modern 1D LTE Spectral Synthesis Package by Adam J. Wheeler, Matthew W. Abruzzo, Andrew R. Casey, Melissa K. Ness

“…Korg is 1–100 times faster than other codes in typical use, compatible with automatic differentiation libraries, and easily extensible, making it ideal for statistical inference and parameter estimation applied to large data sets. …”
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A neural network based global traveltime function (GlobeNN) by Mohammad H. Taufik, Umair bin Waheed, Tariq A. Alkhalifah

“…The traveltime gradients in the loss function are computed efficiently using automatic differentiation, while the P-wave velocity is obtained from the vertically polarized P-wave velocity of the GLAD-M25 model. …”
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Seismic Wave Propagation and Inversion with Neural Operators by Yan Yang, Angela F. Gao, Jorge C. Castellanos, Zachary E. Ross, Kamyar Azizzadenesheli, Robert W. Clayton

“…We illustrate the method with the 2D acoustic wave equation and demonstrate the method’s applicability to seismic tomography, using reverse-mode automatic differentiation to compute gradients of the wavefield with respect to the velocity structure. …”
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Sensitivity of the Ross Ice Shelf to environmental and glaciological controls by F. Baldacchino, M. Morlighem, M. Morlighem, N. R. Golledge, H. Horgan, A. Malyarenko, A. Malyarenko

“…In this paper, we use automatic differentiation and the Ice Sheet and Sea-level System Model to quantify the sensitivity of the RIS to changes in basal friction, ice rigidity, surface mass balance, and basal melting. …”
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