Apostolos Psaros

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in...

A novel formalism of the Wiener path integral (WPI) technique for determining the stochastic response of diverse dynamical systems is developed. It can be construed as a generalization of earlier efforts to account, in a direct manner, also for systems with non-Markovian response processes. Specifically, first, the probability of a path and the ass...

Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different fields, such as computer vision, natural language processing, and the need for reliable tools in risk-sensitive applications. Recently, various machine learning models have al...

A Wiener path integral (WPI) technique is developed for determining the stochastic response of multi-degree-of-freedom (MDOF) nonlinear systems. Specifically, the nonlinear system response joint transition probability density function (PDF) is expressed as a WPI over the space of paths satisfying the initial and final conditions in time. Next, a fu...

We propose a meta-learning technique for offline discovery of physics-informed neural network (PINN) loss functions. We extend earlier works on meta-learning, and develop a gradient-based meta-learning algorithm for addressing diverse task distributions based on parametrized partial differential equations (PDEs) that are solved with PINNs. Furtherm...

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in...

The Wiener path integral (WPI) technique for determining the stochastic response of diverse nonlinear systems is enhanced herein based on a Bayesian compressive sampling (CS) treatment. Specifically, first, sparse expansions for the system response joint probability density function (PDF) are employed. Next, exploiting the localization capabilities...

We propose a meta-learning technique for offline discovery of physics-informed neural network (PINN) loss functions. We extend earlier works on meta-learning, and develop a gradient-based meta-learning algorithm for addressing diverse task distributions based on parametrized partial differential equations (PDEs) that are solved with PINNs. Furtherm...

A methodology based on the Wiener path integral technique (WPI) is developed for stochastic response determination and reliability-based design optimization of a class of nonlinear electromechanical energy harvesters endowed with fractional derivative elements. In this regard, first, the WPI technique is appropriately adapted and enhanced to accoun...

A novel Wiener path integral (WPI) technique is developed for determining the response of stochastically excited nonlinear oscillators. This is done by employing functional series expansions in conjunction with quadratic approximations. The technique can be construed as an extension and enhancement in terms of accuracy of the standard (semiclassica...

The Wiener path integral (WPI) approximate semi-analytical technique for determining the joint response probability density function (PDF) of stochastically excited nonlinear oscillators is generalized herein to account for systems with singular diffusion matrices. Indicative examples include (but are not limited to) systems with only some of their...

The exact joint response transition probability density function (PDF) of linear multi-degree-of-freedom oscillators under Gaussian white noise is derived in closed-form based on the Wiener path integral (WPI) technique. Specifically, in the majority of practical implementations of the WPI technique, only the first couple of terms are retained in t...

A novel approximate technique based on Wiener path integrals (WPIs) is developed for determining, in a computationally efficient manner, the non-stationary joint response probability density function (PDF) of nonlinear multi-degree-of-freedom dynamical systems. Specifically, appropriate multi-dimensional (time-dependent) global bases are constructe...

The recently developed Wiener Path Integral (WPI) technique for determining the joint response probability density function of nonlinear systems subject to Gaussian white noise excitation is generalized herein to account for non-white, non-Gaussian, and non-stationary excitation processes. Specifically, modeling the excitation process as the output...

The standard implementation of the recently developed Wiener path integral (WPI) technique for determining the stochastic response of diverse dynamic systems can be computationally cumbersome, especially for high-dimensional problems. To decrease the computational cost, an enhanced WPI technique formulation was recently proposed by Kougioumtzoglou...

The recently developed Wiener Path Integral (WPI) technique for determining the joint response probability density function of stochastically excited nonlinear systems is extended herein to account for systems with singular diffusion matrices. Among others, indicative examples include partially forced systems, hysteresis modeling via additional aux...

A methodology based on the Wiener path integral technique (WPI) is developed for stochastic response determination and optimization of a class of nonlinear electromechanical energy harvesters. To this aim, first, the WPI technique is extended to address the particular form of the coupled electromechanical governing equations, which possess a singul...

A methodology based on the Wiener path integral technique (WPI) is developed for stochastic response determination and optimization of a class of nonlinear electromechanical energy harvesters. To this aim, first, the WPI technique is extended to address the particular form of the coupled electromechanical governing equations, which possess a singul...

In seismic retrofitting of concrete buildings, frame bays are converted into reinforced concrete (RC) walls by infilling the space between the frame members with RC of a thickness of not more than their width. The cyclic behavior of the resulting wall depends on the connection between the RC infill and the surrounding RC members. The paper uses the...