Related papers: Automatic differentiation and the optimization of …
Simulation and modeling are essential in product development, integrated into the design and manufacturing process to enhance efficiency and quality. They are typically represented as complex nonlinear differential algebraic equations. The…
Dynamic Optimization Problems (DOPs) are challenging to address due to their complex nature, i.e., dynamic environment variation. Evolutionary Computation methods are generally advantaged in solving DOPs since they resemble dynamic…
Quality-Diversity optimization is a new family of optimization algorithms that, instead of searching for a single optimal solution to solving a task, searches for a large collection of solutions that all solve the task in a different way.…
The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…
Trajectory optimization methods have achieved an exceptional level of performance on real-world robots in recent years. These methods heavily rely on accurate analytical models of the dynamics, yet some aspects of the physical world can…
Simulation-based optimization using agent-based models is typically carried out under the assumption that the gradient describing the sensitivity of the simulation output to the input cannot be evaluated directly. To still apply…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
Exascale computing holds great opportunities for molecular dynamics (MD) simulations. However, to take full advantage of the new possibilities, we must learn how to focus computational power on the discovery of complex molecular mechanisms,…
Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and…
Recent applications of machine learning and statistical inference provide case studies demonstrating how such approaches can accelerate the discovery process in physical chemistry and related fields. Examples discussed in this review…
Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…
Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in…
Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling…
Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and…
Biological neural networks can perform complex computations to predict their environment, far above the limited predictive capabilities of individual neurons. While conventional approaches to understanding these computations often focus on…
Differentiation is a cornerstone of computing and data analysis in every discipline of science and engineering. Indeed, most fundamental physics laws are expressed as relationships between derivatives in space and time. However, derivatives…
In this paper we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of Differential Evolution is derived. It is then demonstrated that, under some assumptions on the…
Automatic differentiation is a key component in deep learning. This topic is well studied and excellent surveys such as Baydin et al. (2018) have been available to clearly describe the basic concepts. Further, sophisticated implementations…
Accurate derivatives are important for efficiently locally traversing and converging in quantum optimization landscapes. By deriving analytically exact control derivatives (gradient and Hessian) for unitary control tasks, we show here that…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…