KA-CRNNs learn pressure-dependent and collider-specific kinetic rate laws from data using Kolmogorov-Arnold activations inside a CRNN framework, outperforming interpolative methods by 2.88x in MSE on two proof-of-concept reactions.
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Forward-Mode Automatic Differentiation in Julia
15 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We present ForwardDiff, a Julia package for forward-mode automatic differentiation (AD) featuring performance competitive with low-level languages like C++. Unlike recently developed AD tools in other popular high-level languages such as Python and MATLAB, ForwardDiff takes advantage of just-in-time (JIT) compilation to transparently recompile AD-unaware user code, enabling efficient support for higher-order differentiation and differentiation using custom number types (including complex numbers). For gradient and Jacobian calculations, ForwardDiff provides a variant of vector-forward mode that avoids expensive heap allocation and makes better use of memory bandwidth than traditional vector mode. In our numerical experiments, we demonstrate that for nontrivially large dimensions, ForwardDiff's gradient computations can be faster than a reverse-mode implementation from the Python-based autograd package. We also illustrate how ForwardDiff is used effectively within JuMP, a modeling language for optimization. According to our usage statistics, 41 unique repositories on GitHub depend on ForwardDiff, with users from diverse fields such as astronomy, optimization, finite element analysis, and statistics. This document is an extended abstract that has been accepted for presentation at the AD2016 7th International Conference on Algorithmic Differentiation.
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representative citing papers
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A new stochastic differential dynamic programming method optimizes coupled trajectory design and orbit determination under partial observability, producing navigation-aware solutions with lower fuel consumption than deterministic local optimization in examples like the circular restricted three-body
An admissible Lax-Wendroff flux reconstruction method with automatic differentiation and subcell blending enables robust high-order simulations of relativistic hydrodynamics on adaptive curved meshes.
KA-CRNN learns continuous SOC-dependent kinetic parameters for cathode-electrolyte decomposition directly from DSC data, reproducing heat-release features across all SOCs for NCA, NM, and NMA cathodes.
A PINN learns higher-order corrections to the TaylorT4 PN model from eight NR surrogate waveforms, reducing phase and amplitude errors in the inspiral while enforcing physical symmetries.
AGMCTS augments MCTS with action-score gradients for particle beliefs, a Multiple Importance Sampling tree for reuse, and Area Formula gradients for smooth models, outperforming prior sample-based solvers on continuous benchmarks.
Constrained policy optimization for stochastic optimal control under nonstationary uncertainties via Markov embeddability and finite approximation.
Four finite volume schemes based on different flux formulations are proposed for a degenerated drift-diffusion system, with stability and existence shown for all four and convergence proven for two, plus numerical experiments.
A method for adjoint differentiation of stencil loops that preserves their structure and parallelizability via combined AD and loop transformations, released as the PerforAD tool with seismic and CFD test cases.
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Differentiable GRMHD image sensitivities create a structured error landscape that supports gradient-based parameter recovery for black hole imaging under idealized and noisy conditions.
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Universal Differential Equations for Scientific Machine Learning
Universal Differential Equations unify scientific models with machine learning by embedding flexible approximators into differential equations, enabling applications from biological mechanism discovery to high-dimensional optimization.
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Stochastic Differential Dynamic Programming for Trajectory Optimization under Partial Observability
A new stochastic differential dynamic programming method optimizes coupled trajectory design and orbit determination under partial observability, producing navigation-aware solutions with lower fuel consumption than deterministic local optimization in examples like the circular restricted three-body
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Sensitivities of Black Hole Images from GRMHD Simulations
Differentiable GRMHD image sensitivities create a structured error landscape that supports gradient-based parameter recovery for black hole imaging under idealized and noisy conditions.