Tag
提出一种与坐标系无关的自动微分形式化方法，将几何代数作为代数数据引入 AD，使得单一的基无关导数算子能够表示多种几何微分算子，并可与 JAX 的批处理、编译和硬件加速组合使用，应用于科学 AI 中的流形算子和时空反问题管线。
This paper compares Fourier spectral differentiation and spatial automatic differentiation in periodic physics-informed neural networks, finding that Fourier methods achieve significant training speedups and memory reductions without compromising accuracy.
This paper presents AD-TLERT, a unified GPU-accelerated framework for time-lapse electrical resistivity tomography inversion based on automatic differentiation, enabling efficient and flexible hydrologic monitoring with significant speedup.
This paper traces step-by-step how PyTorch's automatic differentiation engine computes gradients for Physics-Informed Neural Network training, including the two levels of differentiation needed for physics residuals and parameter gradients, using a simple MLP and ODE example.
This documentation introduces hijax types, a new feature in JAX that allows defining custom types with their own invariants, tangent types, batching, and sharding behavior, illustrated with an example of quantized arrays.
This blog post contrasts differential calculus (analysis) as algorithmic and easy with integral calculus (synthesis) as non-algorithmic and difficult, drawing parallels to broader themes in mathematics, computer science, and AI training via automatic differentiation.
Microcrad reimplements Karpathy's micrograd autograd engine in C, providing an educational scalar-valued automatic differentiation library with reference counting and a small neural network, aimed at understanding backpropagation at the scalar level.
A free 57-minute resource by MIT's Applied Math team covers matrix calculations and automatic differentiation for quants and optimization, highlighting Jane Street's high compensation for such skills.
This paper presents acopula, a JAX-native framework for nested Archimedean copula inference that handles arbitrary censoring, nesting trees, and exact parameter gradients using Taylor-mode automatic differentiation, achieving significant speedups over existing methods.
This paper presents methods for differentiable parameter optimization of differential-algebraic equations (DAEs) with state-dependent events, comparing automatic differentiation through simulation with explicit discrete-adjoint methods.