Related papers: Hessian Chain Bracketing
Computations have helped elucidate the dynamics of Earth's mantle for several decades already. The numerical methods that underlie these simulations have greatly evolved within this time span, and today include dynamically changing and…
Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) finds meaningful patterns in spatial data by considering density and spatial proximity. As the clustering algorithm is inherently designed for static…
Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…
The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…
Benchmark experiments are required to test, compare, tune, and understand optimization algorithms. Ideally, benchmark problems closely reflect real-world problem behavior. Yet, real-world problems are not always readily available for…
Dataset condensation can be used to reduce the computational cost of training multiple models on a large dataset by condensing the training dataset into a small synthetic set. State-of-the-art approaches rely on matching the model gradients…
In this work we develop Curvature Propagation (CP), a general technique for efficiently computing unbiased approximations of the Hessian of any function that is computed using a computational graph. At the cost of roughly two gradient…
Combinatorial optimization problems arise in a wide range of applications from diverse domains. Many of these problems are NP-hard and designing efficient heuristics for them requires considerable time and experimentation. On the other…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB…
We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…
This thesis investigates Merton's portfolio problem under two different rough Heston models, which have a non-Markovian structure. The motivation behind this choice of problem is due to the recent discovery and success of rough volatility…
New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: Stochastic approximation replaces regression in the LSM algorithm; Explicit…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
Direct collocation methods are widely used numerical techniques for solving optimal control problems. The discretization of continuous-time optimal control problems transforms them into large-scale nonlinear programming problems, which…
A new perturbation and continuation method is presented for computing and analyzing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $F \equiv J \times B - \nabla p = 0$, and an…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
Estimating causal interactions in complex dynamical systems is an important problem encountered in many fields of current science. While a theoretical solution for detecting the causal interactions has been previously formulated in the…