Related papers: Operator learning without the adjoint

In this paper, we provide a theoretical analysis of a type of operator learning method without data reliance based on the classical finite element approximation, which is called the finite element operator network (FEONet). We first…

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these…

The purpose of this note is to show how some results from the theory of partial differential equations apply to the study of pseudo-spectra of non-self-adjoint operators, which is a topic of current interest in applied mathematics.

This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-differential operators can be approximated in a compressed…

Before a car-following model can be applied in practice, it must first be validated against real data in a process known as calibration. This paper discusses the formulation of calibration as an optimization problem, and compares different…

In this study, we present a tensor--train framework for nonintrusive operator inference aimed at learning discrete operators and using them to predict solutions of physical governing equations. Our framework comprises three approaches:…

Humans have a remarkable ability to disentangle complex sensory inputs (e.g., image, text) into simple factors of variation (e.g., shape, color) without much supervision. This ability has inspired many works that attempt to solve the…

We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not…

We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator $L$, without assuming the gradient estimate for its spectral kernel. The result applies to the cases…

In this article we develop a functional model for a general maximal dissipative operator. We construct the selfadjoint dilation of such operators. Unlike previous functional models, our model is given explicitly in terms of parameters of…

We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…

We study the problem of learning the utility functions of no-regret learning agents in a repeated normal-form game. Differing from most prior literature, we introduce a principal with the power to observe the agents playing the game, send…

Simulating multi-scale phenomena such as turbulent fluid flows is typically computationally very expensive. Filtering the smaller scales allows for using coarse discretizations, however, this requires closure models to account for the…

Language models (LMs) can produce texts that appear accurate and coherent but contain untruthful or toxic content. Inference-time interventions that edit the hidden activations have shown promising results in steering the LMs towards…

We study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection and variational regularization can…

We present a semi-supervised learning algorithm for learning discrete factor analysis models with arbitrary structure on the latent variables. Our algorithm assumes that every latent variable has an "anchor", an observed variable with only…

Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Approximate operators, learned from data, can serve as efficient…

It is well known that the standard projection methods allow one to recover the whole spectrum of a bounded self-adjoint operator but they often lead to spectral pollution, i.e. to spurious eigenvalues lying in the gaps of the essential…

With the growing use of machine learning algorithms and ubiquitous sensors, many `perception-to-control' systems are being developed and deployed. To ensure their trustworthiness, improving their robustness through adversarial training is…

In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…