Related papers: Computer-Aided Derivation of Multi-scale Models: A…
This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…
The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of micro- and nanosystems. In this domain a model is a partial differential equation. Multiscale…
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…
We study normalisation of multistep strategies, strategies that reduce a set of redexes at a time, focussing on the notion of necessary sets, those which contain at least one redex that cannot be avoided in order to reach a normal form.…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
The empirical success of machine learning models with many more parameters than measurements has generated an interest in the theory of overparameterisation, i.e., underdetermined models. This paradigm has recently been studied in domains…
This paper studies the problem of modeling complex domains of actions and change within high-level action description languages. We investigate two main issues of concern: (a) can we represent complex domains that capture together different…
In the dynamic analysis of structural engineering systems, it is common practice to introduce damping models to reproduce experimentally observed features. These models, for instance Rayleigh damping, account for the damping sources in the…
We introduce a mathematical framework for retrosynthetic analysis, an important research method in synthetic chemistry. Our approach represents molecules and their interaction using string diagrams in layered props - a recently introduced…
This work presents a method to adaptively refine reduced-order models \emph{a posteriori} without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive $h$-refinement: it enriches the reduced-basis space…
Computational models of complex systems are usually elaborate and sensitive to implementation details, characteristics which often affect their verification and validation. Model replication is a possible solution to this issue. It avoids…
Stochastic differential equations have been an important tool in modeling complex financial relations, equipped with the possibility of being multidimensional to better oversee complexities inherent in finance. This multidimensionality,…
In real-world scenarios, many data processing problems often involve heterogeneous images associated with different imaging modalities. Since these multimodal images originate from the same phenomenon, it is realistic to assume that they…
In ultrahigh dimensional setting, independence screening has been both theoretically and empirically proved a useful variable selection framework with low computation cost. In this work, we propose a two-step framework by using marginal…
Reasoning tasks are crucial in many domains, especially in science and engineering. Although large language models (LLMs) have made progress in reasoning tasks using techniques such as chain-of-thought and least-to-most prompting, these…
Model-agnostic tools for interpreting machine-learning models struggle to summarize the joint effects of strongly dependent features in high-dimensional feature spaces, which play an important role in pattern recognition, for example in…
We propose a software framework based on the ideas of the Learning-Compression (LC) algorithm, that allows a user to compress a neural network or other machine learning model using different compression schemes with minimal effort.…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…