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Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation (PDE) solvers. However, most existing operator learning methods assume that the…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
We describe a new operator space structure on $L_p$ when $p$ is an even integer and compare it with the one introduced in our previous work using complex interpolation. For the new structure, the Khintchine inequalities and Burkholder's…
The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to…
The Laplace-Beltrami operator (LBO) is a fundamental object associated to Riemannian manifolds, which encodes all intrinsic geometry of the manifolds and has many desirable properties. Recently, we proposed a novel numerical method, Point…
A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a…
Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for…
This paper seeks to extend the theory of composition operators on analytic functional Hilbert spaces from analytic symbols to quasiconformal ones. The focus is the boundedness but operator-theoretic questions are discussed as well. In…
The Descriptor System Tools (DSTOOLS) is a collection of MATLAB functions for the operation on and manipulation of rational transfer function matrices via their descriptor system realizations. The DSTOOLS collection relies on the Control…
Modern vertical take-off and landing vehicles (VTOLs) could significantly affect the future of mobility. The broad range of their application fields encompasses urban air mobility, transportation and logistics as well as reconnaissance and…
Operator learning for partial differential equations (PDEs) aims to learn solution operators on infinite-dimensional function spaces from finite-resolution data. In this setting, it is important for the learned model to be…
A recursion operator is an integro-differential operator which maps a generalized symmetry of a nonlinear PDE to a new symmetry. Therefore, the existence of a recursion operator guarantees that the PDE has infinitely many higher-order…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…
Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers because the expertise…
Convex optimization is an essential tool for machine learning, as many of its problems can be formulated as minimization problems of specific objective functions. While there is a large variety of algorithms available to solve convex…
I present new features of the open-source Python package lips, which leverages the newly developed pyadic and syngular libraries. These developments enable the generation and manipulation of massless phase-space configurations beyond real…
Real-world machine learning on tabular data relies on complex data preparation pipelines for prediction, data integration, augmentation, and debugging. Designing these pipelines requires substantial domain expertise and engineering effort,…
\textbf{FlexBox} is a flexible MATLAB toolbox for finite dimensional convex variational problems in image processing and beyond. Such problems often consist of non-differentiable parts and involve linear operators. The toolbox uses a…
This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming (MICP) problems to global optimality. The proposed scheme uses an iterative…