Related papers: Automating Variational Differentiation
We study a class of filters -- discrete finite-state transition systems employed as incremental stream transducers -- that have application to robotics: e.g., to model combinatorial estimators and also as concise encodings of feedback…
Inverse design of complex flows is notoriously challenging because of the high cost of high dimensional optimization. Usually, optimization problems are either restricted to few control parameters, or adjoint-based approaches are used to…
Selecting powerful predictors for an outcome is a cornerstone task for machine learning. However, some types of questions can only be answered by identifying the predictors that causally affect the outcome. A recent approach to this causal…
Finite difference schemes, using Backward Differentiation Formula (BDF), are studied for the approximation of one-dimensional diffusion equations with an obstacle term, of the form $$\min(v_t - a(t,x) v_{xx} + b(t,x) v_x + r(t,x) v, v-…
The proliferation of computing devices has brought about an opportunity to deploy machine learning models on new problem domains using previously inaccessible data. Traditional algorithms for training such models often require data to be…
We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…
We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems with probabilistic performance guarantees. We employ automatic differentiation to obtain direct policy…
Quantum solutions to differential equations represent quantum data -- states that contain relevant information about the system's behavior, yet are difficult to analyze. We propose a toolbox for reading out information from such data, where…
We propose a novel approach to solving input- and state-constrained parametric mixed-integer optimal control problems using Differentiable Predictive Control (DPC). Our approach follows the differentiable programming paradigm by learning an…
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…
The Harmonic Balance-Alternating Frequency-Time domain (HB-AFT) method is extensively employed for dynamic response analysis of nonlinear systems. However, its application to high-dimensional complex systems is constrained by the manual…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
Forward Automatic Differentiation (AD) is a technique for augmenting programs to compute derivatives. The essence of Forward AD is to attach perturbations to each number, and propagate these through the computation. When derivatives are…
Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables.…
Machine learning models are a powerful theoretical tool for analyzing data from quantum simulators, in which results of experiments are sets of snapshots of many-body states. Recently, they have been successfully applied to distinguish…
Differentiable programming is the combination of classical neural networks modules with algorithmic ones in an end-to-end differentiable model. These new models, that use automatic differentiation to calculate gradients, have new learning…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…
This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…
Variational design is a well-recognized CAD technique due to the increased design efficiency. It often presents as a parametric family of CAD models. Although effective, this way of working cannot handle design requirements that go beyond…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…