Related papers: Barrier Functionals for Output Functional Estimati…
In this paper we propose a novel semi-definite programming approach that solves reach-avoid problems over open (i.e., not bounded a priori) time horizons for dynamical systems modeled by polynomial stochastic differential equations. The…
We introduce an algorithm based on semidefinite programming that yields increasing (resp. decreasing) sequences of lower (resp. upper) bounds on polynomial stationary averages of diffusions with polynomial drift vector and diffusion…
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
Barrier function-based inequality constraints are a means to enforce safety specifications for control systems. When used in conjunction with a convex optimization program, they provide a computationally efficient method to enforce safety…
We consider a nonlinear control affine system controlled by inputs generated by a quadratic program (QP) induced by a control barrier functions (CBF). Specifically, we slightly modify the condition satisfied by CBFs and study how the…
We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows…
We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…
In this paper, we introduce a new approach to constructing unbiased estimators when computing expectations of path functionals associated with stochastic differential equations (SDEs). Our randomization idea is closely related to…
The paper is concerned with functional type a posteriori estimates for the initial boundary value problem for a parabolic partial differential equation with an obstacle. We deduce a guaranteed and computable bound of the distance between…
We propose a functional accelerated failure time model to characterize effects of both functional and scalar covariates on the time to event of interest, and provide regularity conditions to guarantee model identifiability. For efficient…
We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…
As is known, an option price is a solution to a certain partial differential equation (PDE) with terminal conditions (payoff functions). There is a close association between the solution of PDE and the solution of a backward stochastic…
The Scaled Boundary Finite Element Method (SBFEM) is a technique in which approximation spaces are constructed using a semi-analytical approach. They are based on partitions of the computational domain by polygonal/polyhedral subregions,…
By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…
We present algorithms and their implementation to compute limit cycles and their isochrons for state-dependent delay equations (SDDE's) which are perturbed from a planar differential equation with a limit cycle. Note that the space of…
A multi-agent partially observable Markov decision process (MPOMDP) is a modeling paradigm used for high-level planning of heterogeneous autonomous agents subject to uncertainty and partial observation. Despite their modeling efficiency,…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
A longstanding problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors. We present a framework to compute lower bounds on largest absolute roundoff errors, for a…
We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be amenable or even to have computable projections, two previously challenging…