Georgios Arampatzis

Ivica Kičić, Pantelis R. Vlachas, Georgios Arampatzis et al.

Predictive simulations are essential for applications ranging from weather forecasting to material design. The veracity of these simulations hinges on their capacity to capture the effective system dynamics. Massively parallel simulations predict the systems dynamics by resolving all spatiotemporal scales, often at a cost that prevents experimentation. On the other hand, reduced order models are fast but often limited by the linearization of the system dynamics and the adopted heuristic closures. We propose a novel systematic framework that bridges large scale simulations and reduced order models to extract and forecast adaptively the effective dynamics (AdaLED) of multiscale systems. AdaLED employs an autoencoder to identify reduced-order representations of the system dynamics and an ensemble of probabilistic recurrent neural networks (RNNs) as the latent time-stepper. The framework alternates between the computational solver and the surrogate, accelerating learned dynamics while leaving yet-to-be-learned dynamics regimes to the original solver. AdaLED continuously adapts the surrogate to the new dynamics through online training. The transitions between the surrogate and the computational solver are determined by monitoring the prediction accuracy and uncertainty of the surrogate. The effectiveness of AdaLED is demonstrated on three different systems - a Van der Pol oscillator, a 2D reaction-diffusion equation, and a 2D Navier-Stokes flow past a cylinder for varying Reynolds numbers (400 up to 1200), showcasing its ability to learn effective dynamics online, detect unseen dynamics regimes, and provide net speed-ups. To the best of our knowledge, AdaLED is the first framework that couples a surrogate model with a computational solver to achieve online adaptive learning of effective dynamics. It constitutes a potent tool for applications requiring many expensive simulations.

Georgios Arampatzis, Daniel Wälchli, Panagiotis Angelikopoulos et al.

We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin transition kernels with the advantages of global exploration by a population based sampling algorithm, the Transitional Markov Chain Monte Carlo (TMCMC). The Langevin diffusion process is determined by either the Hessian or the Fisher Information of the target distribution with appropriate modifications for non positive definiteness. The present methods is shown to be superior over other population based algorithms, in sampling probability distributions for which gradients are available and is shown to handle otherwise unidentifiable models. We demonstrate the capabilities and advantages of the method in computing the posterior distribution of the parameters in a Pharmacodynamics model, for glioma growth and its drug induced inhibition, using clinical data.

Georgios Arampatzis, Markos A. Katsoulakis, Luc Rey-Bellet

We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher Information Matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithms without additional modifications.

Georgios Arampatzis, Markos A. Katsoulakis, Yannis Pantazis

The instantaneous relative entropy (IRE) and the corresponding instanta- neous Fisher information matrix (IFIM) for transient stochastic processes are pre- sented in this paper. These novel tools for sensitivity analysis of stochastic models serve as an extension of the well known relative entropy rate (RER) and the corre- sponding Fisher information matrix (FIM) that apply to stationary processes. Three cases are studied here, discrete-time Markov chains, continuous-time Markov chains and stochastic differential equations. A biological reaction network is presented as a demonstration numerical example.

Georgios Arampatzis, Avi Arampatzis

Humour-aware information retrieval poses unique challenges beyond standard semantic retrieval, as systems must account not only for topical relevance but also for humour-specific linguistic phenomena such as wordplay, phonetic ambiguity, and polysemy. In this paper, Team DUTH studies multilingual humour-aware information retrieval using the CLEF 2025 JOKER Task 1 benchmark, which evaluates humour retrieval in English and Portuguese. Our approach combines multilingual XLM-RoBERTa-based dense retrieval with additional system variants, including neural re-ranking, in order to assess the extent to which general-purpose Transformer models can capture humour-specific relevance. The results reveal substantial cross-lingual variation. While the Portuguese runs demonstrate comparatively strong performance across MAP, MRR, and early precision metrics, the English runs perform significantly worse, with relevant humorous documents frequently appearing at lower ranks. These findings highlight the limitations of purely semantic dense representations for humour retrieval, particularly when humour depends on surface-level cues that are not explicitly modelled by multilingual encoders. We further analyse contributing factors to this discrepancy, including dataset characteristics, query-document alignment, and variation in humour mechanisms. Overall, the Team DUTH experiments establish multilingual dense-retrieval and re-ranking baselines and provide insights into the challenges of modelling humour-aware relevance within the JOKER framework.

Georgios Arampatzis, Stylianos Katsarakis, Charalambos Makridakis

The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by incorporating probabilistic frameworks to effectively model uncertainty in complex systems. Our approach enhances the representation of uncertainty in forward problems by combining generative modeling techniques with PINNs. This integration enables in a systematic fashion uncertainty control while maintaining the predictive accuracy of the model. We demonstrate the utility of this method through applications to random differential equations and random partial differential equations (PDEs).

Pantelis R. Vlachas, Georgios Arampatzis, Caroline Uhler et al.

Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively parallel simulations predict the system dynamics by resolving all spatiotemporal scales, often at a cost that prevents experimentation while their findings may not allow for generalisation. On the other hand reduced order models are fast but limited by the frequently adopted linearization of the system dynamics and/or the utilization of heuristic closures. Here we present a novel systematic framework that bridges large scale simulations and reduced order models to Learn the Effective Dynamics (LED) of diverse complex systems. The framework forms algorithmic alloys between non-linear machine learning algorithms and the Equation-Free approach for modeling complex systems. LED deploys autoencoders to formulate a mapping between fine and coarse-grained representations and evolves the latent space dynamics using recurrent neural networks. The algorithm is validated on benchmark problems and we find that it outperforms state of the art reduced order models in terms of predictability and large scale simulations in terms of cost. LED is applicable to systems ranging from chemistry to fluid mechanics and reduces the computational effort by up to two orders of magnitude while maintaining the prediction accuracy of the full system dynamics. We argue that LED provides a novel potent modality for the accurate prediction of complex systems.