arXiv subjects

Michail Kavousanakis

Publications and source records attributed to Michail Kavousanakis.

4 recordsLinked to original sources

arXiv2026

A Bayesian-optimization framework coupling a multiphase PDE tumor model to efficiently design combination therapy schedules

Designing combination cancer therapies requires choosing not only which agents to combine but also their relative doses and timing decisions that critically shape the trade-off between efficacy and toxicity. High-fidelity mechanistic models of tumor growth, formulated as systems of coupled PDEs, can in principle resolve how these scheduling choices interact with the tumor microenvironment, but each evaluation is computationally expensive, rendering brute-force exploration of the design space intractable. We present a Bayesian Optimization framework that treats a multiphase, vascularized, two-dimensional PDE tumor simulator as a black box and uses a Gaussian-process surrogate to find schedules that maximize therapeutic outcomes within a small budget of expensive simulations. We orchestrate the COMSOL Multiphysics solver from Python, producing a fully automated optimization loop in which a single simulation of ~650 days of tumor evolution requires roughly 80 hours of wall time. The framework is applied to three clinically relevant scenarios: (i) a two-agent regimen (docetaxel + bevacizumab), (ii) a three-agent regimen (docetaxel + bevacizumab + radiation) under reduced and full intensity, and (iii) a single-agent dose-fractionation problem in which efficacy is balanced against healthy-tissue toxicity through a weighted multi-objective formulation. The BO loop converges to clinically plausible optima with one to two orders of magnitude fewer simulations than an equivalent grid search, identifies docetaxel-induced radiosensitization as a decisive factor in the triple-therapy optimum, and recovers a fractionation regime consistent with clinical protocols when both efficacy and toxicity are considered. The framework is agnostic to the specifics of the underlying PDE model and provides a transferable methodology for design optimization of expensive engineered or biological simulators.

q-bio.TO↗

arXiv2025

A Physics Informed Machine Learning Framework for Optimal Sensor Placement and Parameter Estimation

Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that provide the maximum amount of information about the unknown parameters, in particular for the case of distributed-parameter systems, where spatial variations are important. Physics-Informed Neural Networks (PINNs) have recently emerged as a powerful machine-learning (ML) tool for parameter estimation, particularly in cases with sparse or noisy measurements, overcoming some of the limitations of traditional optimization-based and Bayesian approaches. Despite the widespread use of PINNs for solving inverse problems, relatively little attention has been given to how their performance depends on sensor placement. This study addresses this gap by introducing a comprehensive PINN-based framework that simultaneously tackles optimal sensor placement and parameter estimation. Our approach involves training a PINN model in which the parameters of interest are included as additional inputs. This enables the efficient computation of sensitivity functions through automatic differentiation, which are then used to determine optimal sensor locations exploiting the D-optimality criterion. The framework is validated on two illustrative distributed-parameter reaction-diffusion-advection problems of increasing complexity. The results demonstrate that our PINNs-based methodology consistently achieves higher accuracy compared to parameter values estimated from intuitively or randomly selected sensor positions.

stat.ML↗

arXiv2025

Going with the Flow: Solving for Symmetry-Driven PDE dynamics with Physics-informed Neural Networks

In the past, we have presented a systematic computational framework for analyzing self-similar and traveling wave dynamics in nonlinear partial differential equations (PDEs) by dynamically factoring out continuous symmetries such as translation and scaling. This is achieved through the use of time-dependent transformations -- what can be viewed as dynamic pinning conditions -- that render the symmetry-invariant solution stationary or slowly varying in rescaled coordinates. The transformation process yields a modified evolution equation coupled with algebraic constraints on the symmetry parameters, resulting in index-2 differential-algebraic equation (DAE) systems. The framework accommodates both first-kind and second-kind self-similarity, and directly recovers the self-similarity exponents or wave speeds as part of the solution, upon considering steady-state solutions in the rescaled coordinate frame. To solve the resulting high-index DAE systems, we employ Physics-Informed Neural Networks (PINNs), which naturally integrate PDE residuals and algebraic constraints into a unified loss function. This allows simultaneous inference of both the invariant solution and the transformation properties (such as the speed or the scaling rate without the need for large computational domains, mesh adaptivity, or front tracking. We demonstrate the effectiveness of the method on four canonical problems: (i) the Nagumo equation exhibiting traveling waves, (ii) the diffusion equation (1D and 2D) with first-kind self-similarity, (iii) the 2D axisymmetric porous medium equation showcasing second-kind self-similarity, and (iv) the Burgers equation, which involves both translational and scaling invariance. The results demonstrate the capability of PINNs to effectively solve these complex PDE-DAE systems, providing a promising tool for studying nonlinear wave and scaling phenomena.

math.AP↗

arXiv2022

Limits of Entrainment of Circadian Neuronal Networks

Circadian rhythmicity lies at the center of various important physiological and behavioral processes in mammals, such as sleep, metabolism, homeostasis, mood changes and more. It has been shown that this rhythm arises from self-sustained biomolecular oscillations of a neuronal network located in the Suprachiasmatic Nucleus (SCN). Under normal circumstances, this network remains synchronized to the day-night cycle due to signaling from the retina. Misalignment of these neuronal oscillations with the external light signal can disrupt numerous physiological functions and take a long-lasting toll on health and well-being. In this work, we study a modern computational neuroscience model to determine the limits of circadian synchronization to external light signals of different frequency and duty cycle. We employ a matrix-free approach to locate periodic steady states of the high-dimensional model for various driving conditions. Our algorithmic pipeline enables numerical continuation and construction of bifurcation diagrams w.r.t. forcing parameters. We computationally explore the effect of heterogeneity in the circadian neuronal network, as well as the effect of corrective therapeutic interventions, such as that of the drug molecule Longdaysin. Lastly, we employ unsupervised learning to construct a data-driven embedding space for representing neuronal heterogeneity.

q-bio.NC↗