arXiv subjects

Konstantinos Vlachas

Publications and source records attributed to Konstantinos Vlachas.

5 recordsLinked to original sources

arXiv2026

Reduced-Order Physics-Informed Neural Network with Adaptive Basis Refinement for Structural Identification

Physics-informed neural networks (PINNs) provide a flexible framework for solving forward and inverse problems. However, their direct application to structural dynamics remains limited by high system dimensionality and model-form errors arising from incomplete physics. Reduced-order models (ROMs) can alleviate the dimensionality bottleneck, yet existing PINN-ROM couplings typically rely on fixed reduced subspaces, target forward simulations, or assume complete physics, restricting their use for inverse identification under parametric variability or incomplete system knowledge. To address these limitations, this work proposes a Reduced-Order Physics-Informed Neural Network (RO-PINN) framework with adaptive basis refinement for structural identification under known and incomplete physics. Via projection, reduced governing equations are embedded directly into the PINN loss, facilitating learning in a low-dimensional latent space. An adaptive scheme updates the projection basis during training so that the latent space is progressively realigned with evolving structural parameters or learned residual restoring forces. This realignment reduces basis-mismatch errors and limits their influence on the inferred residual force. The method is validated on a four-story steel frame with nonlinear hysteretic braces under sparse and noisy measurements. Results show parameter identification comparable to or more accurate than Bayesian model updating with lower computational cost in the considered cases, recovery of unmodeled nonlinear restoring forces under incomplete physics, and joint identification of residual restoring forces and structural parameters within the same framework. Overall, RO-PINN provides a unified framework for structural identification by integrating reduced-order modeling, adaptive basis refinement, and physics-informed learning within a single formulation.

cs.CE↗

arXiv2026

Beyond Static Models: Hypernetworks for Adaptive and Generalizable Forecasting in Complex Parametric Dynamical Systems

Dynamical systems play a key role in modeling, forecasting, and decision-making across a wide range of scientific domains. However, variations in system parameters, also referred to as parametric variability, can lead to drastically different model behavior and output, posing challenges for constructing models that generalize across parameter regimes. In this work, we introduce the Parametric Hypernetwork for Learning Interpolated Networks (PHLieNet), a framework that simultaneously learns: (a) a global mapping from the parameter space to a nonlinear embedding and (b) a mapping from the inferred embedding to the weights of a dynamics propagation network. The learned embedding serves as a latent representation that modulates a base network, termed the hypernetwork, enabling it to generate the weights of a target network responsible for forecasting the system's state evolution conditioned on the previous time history. By interpolating in the space of models rather than observations, PHLieNet facilitates smooth transitions across parameterized system behaviors, enabling a unified model that captures the dynamic behavior across a broad range of system parameterizations. The performance of the proposed technique is validated in a series of dynamical systems with respect to its ability to extrapolate in time and interpolate and extrapolate in the parameter space, i.e., generalize to dynamics that were unseen during training. Our approach outperforms state-of-the-art baselines in both short-term forecast accuracy and in capturing long-term dynamical features such as attractor statistics.

cs.LG↗

arXiv2025

A Reduced Order Model conditioned on monitoring features for estimation and uncertainty quantification in engineered systems

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM construction, schemes that allow to retain a portion of the physics tend to enhance the interpretability and generalization of ROMs. However, physics-based techniques can adversely scale when dealing with nonlinear systems that feature parametric dependencies. This study introduces a generative physics-based ROM that is suited for nonlinear systems with parametric dependencies and is additionally able to quantify the confidence associated with the respective estimates. A main contribution of this work is the conditioning of these parametric ROMs to features that can be derived from monitoring measurements, feasibly in an online fashion. This is contrary to most existing ROM schemes, which remain restricted to the prescription of the physics-based, and usually a priori unknown, system parameters. Our work utilizes conditional Variational Autoencoders to continuously map the required reduction bases to a feature vector extracted from limited output measurements, while additionally allowing for a probabilistic assessment of the ROM-estimated Quantities of Interest. An auxiliary task using a neural network-based parametrization of suitable probability distributions is introduced to re-establish the link with physical model parameters. We verify the proposed scheme on a series of simulated case studies incorporating effects of geometric and material nonlinearity under parametric dependencies related to system properties and input load characteristics.

cs.CE↗

arXiv2023

VpROM: A novel Variational AutoEncoder-boosted Reduced Order Model for the treatment of parametric dependencies in nonlinear systems

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition, however, such methods can become inefficient or fail in the case of parameteric or strongly nonlinear models. Such limitations are usually tackled via a library of local reduction bases each of which being valid for a given parameter vector. The success of such methods, however, is strongly reliant upon the method used to relate the parameter vectors to the local bases, this is typically achieved using clustering or interpolation methods. We propose the replacement of these methods with a Variational Autoencoder (VAE) to be used as a generative model which can infer the local basis corresponding to a given parameter vector in a probabilistic manner. The resulting VAE-boosted parametric ROM \emph{VpROM} still retains the physical insights of a projection-based method but also allows for better treatment of problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

math.NA↗

arXiv2020

A local basis approximation approach for nonlinear parametric model order reduction

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction (pMOR) scheme for nonlinear structural dynamics, and the particular case of material nonlinearity. A physics-based parametric representation is developed, incorporating dependencies on system properties and/or excitation characteristics. The pMOR formulation relies on use of a Proper Orthogonal Decomposition applied to a series of snapshots of the nonlinear dynamic response. A new approach to manifold interpolation is proposed, with interpolation taking place on the reduced coefficient matrix mapping local bases to a global one. We demonstrate the performance of this approach firstly on the simple example of a shear-frame structure, and secondly on the more complex 3D numerical case study of an earthquake-excited wind turbine tower. Parametric dependence pertains to structural properties, as well as the temporal and spectral characteristics of the applied excitation. The developed parametric Reduced Order Model (pROM) can be exploited for a number of tasks including monitoring and diagnostics, control of vibrating structures, and residual life estimation of critical components.

math.NA↗