相关论文: Comprehensive Framework for Controlling Nonlinear …
Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…
The theory of Wasserstein gradient flows in the space of probability measures has made an enormous progress over the last twenty years. It constitutes a unified and powerful framework in the study of dissipative partial differential…
The propagation of electromagnetic waves in general media is modeled by the time-dependent Maxwell's partial differential equations (PDEs), coupled with constitutive laws that describe the response of the media. In this work, we focus on…
The present study proposes a multi-objective framework for structure selection of nonlinear systems which are represented by polynomial NARX models. This framework integrates the key components of Multi-Criteria Decision Making (MCDM) which…
Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…
Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…
Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…
As the dimension of a system increases, traditional methods for control and differential games rapidly become intractable, making the design of safe autonomous agents challenging in complex or team settings. Deep-learning approaches avoid…
In this paper, we propose a network model, the multiclass classification-based reduced order model (MC-ROM), for solving time-dependent parametric partial differential equations (PPDEs). This work is inspired by the observation of applying…
Despite growing interest in data-driven analysis and control of linear systems, descriptor systems--which are essential for modeling complex engineered systems with algebraic constraints like power and water networks--have received…
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…
Chemical multisensor devices need calibration algorithms to estimate gas concentrations. Their possible adoption as indicative air quality measurements devices poses new challenges due to the need to operate in continuous monitoring modes…
Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…
In this paper we investigate infinite horizon optimal control problems for parametrized partial differential equations. We are interested in feedback control via dynamic programming equations which is well-known to suffer from the curse of…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
Designing sequences that satisfy multiple, often conflicting, objectives is a central challenge in therapeutic and biomolecular engineering. Existing generative frameworks largely operate in continuous spaces with single-objective guidance,…
Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the…
Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here,…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead,…