相关论文: Handling geometrical variability in nonlinear redu…

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a black-box.…

We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach…

Time-dependent partial differential equations are ubiquitous in physics-based modeling, but they remain computationally intensive in many-query scenarios, such as real-time forecasting, optimal control, and uncertainty quantification.…

Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalise…

The domain decomposition (DD) nonlinear-manifold reduced-order model (NM-ROM) represents a computationally efficient method for integrating underlying physics principles into a neural network-based, data-driven approach. Compared to linear…

We present AROMA (Attentive Reduced Order Model with Attention), a framework designed to enhance the modeling of partial differential equations (PDEs) using local neural fields. Our flexible encoder-decoder architecture can obtain smooth…

Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…

Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse and complex molecular and biomolecular datasets due to the limited…

State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…

Continuous monitoring and real-time control of high-dimensional distributed systems are often crucial in applications to ensure a desired physical behavior, without degrading stability and system performances. Traditional feedback control…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However, existing methodologies struggle to combine geometric…

Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced…

In this work the development of a machine learning-based Reduced Order Model (ROM) for the investigation of hemodynamics in a patient-specific configuration of Coronary Artery Bypass Graft (CABG) is proposed. The computational domain is…

Solving and optimising Partial Differential Equations (PDEs) in geometrically parameterised domains often requires iterative methods, leading to high computational and time complexities. One potential solution is to learn a direct mapping…

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

Practical applications of mechanical metamaterials often involve solving inverse problems where the objective is to find the (multiple) microarchitectures that give rise to a given set of properties. The limited resolution of additive…

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…

This work presents a framework for parametric reduction in FEM, where geometry is controlled by a parameter without altering material properties or stress states. The inverse determinant in the weak form is expanded as a power series, with…

Reduced-order modeling (ROM) of time-dependent and parameterized differential equations aims to accelerate the simulation of complex high-dimensional systems by learning a compact latent manifold representation that captures the…