Related papers: Multi-fidelity Learning of Reduced Order Models fo…
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…
Model order reduction usually consists of two stages: the offline stage and the online stage. The offline stage is the expensive part that sometimes takes hours till the final reduced-order model is derived, especially when the original…
Highly accurate datasets from numerical or physical experiments are often expensive and time-consuming to acquire, posing a significant challenge for applications that require precise evaluations, potentially across multiple scenarios and…
In this contribution we device and analyze improved variants of the non-conforming dual approach for trust-region reduced basis (TR-RB) approximation of PDE-constrained parameter optimization that has recently been introduced in [Keil et…
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…
We consider nonlinear inverse problems arising in the context of parameter identification for parabolic partial differential equations (PDEs). For stable reconstructions, regularization methods such as the iteratively regularized…
The Reduced Basis Method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. One critical stage of the \textit{offline} portion of the algorithm is a greedy algorithm, requiring…
A parametric model order reduction (MOR) approach for simulating the high dimensional models arising in financial risk analysis is proposed on the basis of the proper orthogonal decomposition (POD) approach to generate small model…
Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…
Reduced-order models that accurately abstract high fidelity models and enable faster simulation is vital for real-time, model-based diagnosis applications. In this paper, we outline a novel hybrid modeling approach that combines machine…
In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini…
In this contribution we propose and rigorously analyze new variants of adaptive Trust-Region methods for parameter optimization with PDE constraints and bilateral parameter constraints. The approach employs successively enriched Reduced…
We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from…
A multi-fidelity (MF) active learning method is presented for design optimization problems characterized by noisy evaluations of the performance metrics. Namely, a generalized MF surrogate model is used for design-space exploration,…
Deep surrogate models for parametric partial differential equations (PDEs) can deliver high-fidelity approximations but remain prohibitively data-hungry: training often requires thousands of fine-grid simulations, each incurring substantial…
Multi-fidelity Reinforcement Learning (RL) frameworks efficiently utilize computational resources by integrating analysis models of varying accuracy and costs. The prevailing methodologies, characterized by transfer learning, human-inspired…
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,…
There is a recent proliferation of research on the integration of machine learning and optimization. One expansive area within this research stream is predictive-model embedded optimization, which proposes the use of pre-trained predictive…
This work introduces a data-driven, non-intrusive reduced-order modeling (ROM) framework that leverages Optimal Transport (OT) for multi-fidelity and parametric problems in two-phase flows modelling. Building upon the success of…
We present a flexible trust region descend algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective…