Related papers: The Python LevelSet Toolbox (LevelSetPy)
We announce some Python classes for numerical solution of partial differential equations, or boundary value problems of ordinary differential equations. These classes are built on routines in \texttt{numpy} and \texttt{scipy.sparse.linalg}…
Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. The practical implementation of the gradient descent method to bilevel optimization encounters computational…
Obtaining high quality particle distribution representing clean geometry in pre-processing is essential for the simulation accuracy of the particle-based methods. In this paper, several level-set based techniques for cleaning up `dirty'…
This paper was prepared by the HEP Software Foundation (HSF) PyHEP Working Group as input to the second phase of the LHCC review of High-Luminosity LHC (HL-LHC) computing, which took place in November, 2021. It describes the adoption of…
Stochastic physical problems governed by nonlinear conservation laws are challenging due to solution discontinuities in stochastic and physical space. In this paper, we present a level set method to track discontinuities in stochastic space…
Hamilton-Jacobi (HJ) reachability analysis provides a formal method for guaranteeing safety in constrained control problems. It synthesizes a value function to represent a long-term safe set called feasible region. Early synthesis methods…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
This paper introduces pycvxset, a new Python package to manipulate and visualize convex sets. We support polytopes and ellipsoids, and provide user-friendly methods to perform a variety of set operations. For polytopes, pycvxset supports…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…
Finite dimensional solutions to a class of stochastic partial differential equations are obtained extending the differential constraints method for deterministic PDE to the stochastic framework. A geometrical reformulation of the stochastic…
We present an open-source tensor network Python library for quantum many-body simulations. At its core is an abelian-symmetric tensor, implemented as a sparse block structure managed by logical layer on top of dense multi-dimensional array…
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional…
We construct quantum algorithms to compute physical observables of nonlinear PDEs with M initial data. Based on an exact mapping between nonlinear and linear PDEs using the level set method, these new quantum algorithms for nonlinear…
Gaussian Processes (GPs) are flexible, nonparametric Bayesian models widely used for regression and classification because of their ability to capture complex data patterns and quantify predictive uncertainty. However, the O(n^3)…
We introduce Devito, a new domain-specific language for implementing high-performance finite difference partial differential equation solvers. The motivating application is exploration seismology where methods such as Full-Waveform…
In recent years, the efficient numerical solution of Hamiltonian problems has led to the definition of a class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Such methods admit an interesting…
Space-filling experimental design techniques are commonly used in many computer modeling and simulation studies to explore the effects of inputs on outputs. This research presents raxpy, a Python package that leverages expressive annotation…
Providing formal safety and performance guarantees for autonomous systems is becoming increasingly important. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for providing these guarantees, since it can…
Deep learning methods, which exploit auto-differentiation to compute derivatives without dispersion or dissipation errors, have recently emerged as a compelling alternative to classical mesh-based numerical schemes for solving hyperbolic…
Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…