Related papers: Automatic Differentiation in ROOT
Differentiable programming, enabled by automatic differentiation (AD), provides a robust framework for gradient-based optimization in computational plasma physics. While optimization is often only used towards design, we demonstrate that it…
We present a GPU-based system for automatic differentiation (AD) of functions defined on triangle meshes, designed to exploit the locality and sparsity in mesh-based computation. Our system evaluates derivatives using per-element…
Anomaly detection (AD) is a crucial machine learning task that aims to learn patterns from a set of normal training samples to identify abnormal samples in test data. Most existing AD studies assume that the training and test data are drawn…
The extraction of the model parameters is as important as the development of compact model itself because simulation accuracy is fully determined by the accuracy of the parameters used. This study proposes an efficient model-parameter…
Shape optimization approaches to inverse design offer low-dimensional, physically-guided parameterizations of structures by representing them as combinations of shape primitives. However, on discretized rectilinear simulation grids,…
Backpropagation is a classic automatic differentiation algorithm computing the gradient of functions specified by a certain class of simple, first-order programs, called computational graphs. It is a fundamental tool in several fields, most…
Optimization of beamlines and lattices is a common problem in accelerator physics, which is usually solved with semi-analytical methods and numerical optimization routines. However, these are usually of the gradient-free or…
We discuss the calculation of the derivatives of ODE systems with the automatic differentiation tool ADiMat. Using the well-known Lotka-Volterra equations and the ode23 ODE solver as examples we show the analytic derivatives and detail how…
Numerous Optimization Algorithms have a time-varying update rule thanks to, for instance, a changing step size, momentum parameter or, Hessian approximation. In this paper, we apply unrolled or automatic differentiation to a time-varying…
This paper presents an artificial intelligence algorithm that can be used to derive formulas from various scientific disciplines called automatic derivation machine. First, the formula is abstractly expressed as a multiway tree model, and…
We present and evaluate the Futhark implementation of reverse-mode automatic differentiation (AD) for the basic blocks of parallel programming: reduce, prefix sum (scan), and reduce by index. We first present derivations of general-case…
Autonomous driving (AD) agents generate driving policies based on online perception results, which are obtained at multiple levels of abstraction, e.g., behavior planning, motion planning and control. Driving policies are crucial to the…
The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
Software engineering practices such as constructing requirements and establishing traceability help ensure systems are safe, reliable, and maintainable. However, they can be resource-intensive and are frequently underutilized. To alleviate…
Understanding fine-grained object affordances is imperative for robots to manipulate objects in unstructured environments given open-ended task instructions. However, existing methods of visual affordance predictions often rely on manually…
We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…
In this note we derive the backward (automatic) differentiation (adjoint [automatic] differentiation) for an algorithm containing a conditional expectation operator. As an example we consider the backward algorithm as it is used in Bermudan…
This paper proposes a Direct Rational Radial Basis Functions Partition of Unity (D-RRBF-PU) approach to compute derivatives of functions with steep gradients or discontinuities. The novelty of the method concerns how derivatives are…
We propose a new evaluation for automatic solvers for algebra word problems, which can identify mistakes that existing evaluations overlook. Our proposal is to evaluate such solvers using derivations, which reflect how an equation system…