Related papers: A new perspective on hierarchical spline spaces fo…
This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized…
The multi-level hp-refinement scheme is a powerful extension of the finite element method that allows local mesh adaptation without the trouble of constraining hanging nodes. This is achieved through hierarchical high-order overlay meshes,…
Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…
We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…
Adapting the recently developed randomized dyadic structures, we introduce the notion of spline function in geometrically doubling quasi-metric spaces. Such functions have interpolation and reproducing properties as the linear splines in…
We establish the convergence of an adaptive spline-based finite element method of a fourth order elliptic problem.
We present a method for drawing isolines indicating regions of equal joint exceedance probability for bivariate data. The method relies on bivariate regular variation, a dependence framework widely used for extremes. This framework enables…
We extend the result of D. Phillips (On one-homogeneous solutions to elliptic systems in two dimensions. C. R. Math. Acad. Sci. Paris 335 (2002), no. 1, 39-42) by showing that one-homogeneous solutions of certain elliptic systems in…
This work develops a systematic functional-analytic framework for nonlinear adaptive memory, where the influence of past events depends on both elapsed time and the state values along a trajectory. The framework comprises three hierarchical…
Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on…
A hierarchical Model Predictive Control (MPC) formulation is presented for coupled discrete-time linear systems with state and input constraints. Compared to a centralized approach, a two-level hierarchical controller, with one controller…
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…
In this paper, we derive a framework to understand the effect of imperfections on the phasematching spectrum of a wide class of nonlinear systems. We show that this framework is applicable to many physical systems, such as waveguides or…
General purpose agents will require large repertoires of skills. Empowerment -- the maximum mutual information between skills and states -- provides a pathway for learning large collections of distinct skills, but mutual information is…
These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…
Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments. While notable progress has been made, the capabilities of differentiable physics solvers remain limited. We…
This work is focused on constructing space-time covariance functions through a hierarchical mixture approach that can serve as building blocks for capturing complex dependency structures. This hierarchical mixture approach provides a…
A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…
In this paper, we propose a framework for designing sliding mode controllers for a class of mechanical systems with symmetry, both unconstrained and constrained, that evolve on principal fiber bundles. Control laws are developed based on…
The aim of this paper is to prove the existence of multiple solutions for a family of nonlinear elliptic systems in divergence form coupled with a pointwise gradient constraint: \begin{align*} \left\{ \begin{array}{ll}…