arXiv subjects

Serafim Kalliadasis

Publications and source records attributed to Serafim Kalliadasis.

At least 19 recordsLinked to original sources

arXiv2026

Forecasting with an N-dimensional Langevin Equation and a Neural-Ordinary Differential Equation

Accurate prediction of electricity day-ahead prices is essential in competitive electricity markets. Although stationary electricity-price forecasting techniques have received considerable attention, research on non-stationary methods is comparatively scarce, despite the common prevalence of non-stationary features in electricity markets. Specifically, existing non-stationary techniques will often aim to address individual non-stationary features in isolation, leaving aside the exploration of concurrent multiple non-stationary effects. Our overarching objective here is the formulation of a framework to systematically model and forecast non-stationary electricity-price time series, encompassing the broader scope of non-stationary behavior. For this purpose we develop a data-driven model that combines an N-dimensional Langevin equation (LE) with a neural-ordinary differential equation (NODE). The LE captures fine-grained details of the electricity-price behavior in stationary regimes but is inadequate for non-stationary conditions. To overcome this inherent limitation, we adopt a NODE approach to learn, and at the same time predict, the difference between the actual electricity-price time series and the simulated price trajectories generated by the LE. By learning this difference, the NODE reconstructs the non-stationary components of the time series that the LE is not able to capture. We exemplify the effectiveness of our framework using the Spanish electricity day-ahead market as a prototypical case study. Our findings reveal that the NODE nicely complements the LE, providing a comprehensive strategy to tackle both stationary and non-stationary electricity-price behavior. The framework's dependability and robustness is demonstrated through different non-stationary scenarios by comparing it against a range of basic naive methods.

cs.LG↗

arXiv2026

MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning

Neural ordinary differential equations (Neural ODEs) often fit training trajectories while generalizing poorly to unseen initial conditions and long horizons. We propose MPINeuralODE, which combines a soft physics-informed residual with a Multiple-Initial-Condition (MIC) multiple-shooting curriculum whose ingredients are structurally complementary: the physics term anchors the vector-field magnitude on the support that MIC enlarges. We evaluate along three axes: out-of-sample error, long-horizon stability, and Hamiltonian drift, which together expose whether the learned dynamics recover the underlying vector field. On Lotka-Volterra, MPINeuralODE achieves the lowest out-of-sample and long-horizon MSE among data-driven methods, with a 24% reduction over the baseline Neural ODE, while essentially matching the PINN ablation on Hamiltonian drift.

cs.LG↗

arXiv2026

A Finite Element Method for Fluctuating Navier--Stokes Equations

We introduce a finite-element framework for simulating thermal fluctuations in compressible fluids governed by the fluctuating Navier-Stokes equations. The method is designed to preserve the fundamental fluctuation-dissipation balance at the discrete level. This is achieved by defining the stochastic forcing term in the weak formulation, ensuring its covariance is proportional to the discrete viscous dissipation operator. A nodal quadrature rule is employed to eliminate unphysical mesh-scale correlations. The time integration is performed using the Crank-Nicolson scheme to maintain numerical stability and accuracy. The proposed approach is numerically validated in one, two, and three spatial dimensions, demonstrating its capability to correctly capture equilibrium fluctuation statistics across various discretisation parameters.

cond-mat.stat-mech↗

arXiv2026

A Physics-Informed Neural Network with a Modified Lorentzian Activation for Nonlocal Gradient-Flow Equations in Dynamic Density Functional Theory

We develop a physics-informed neural network (PINN) framework for nonlocal partial differential equations arising in dynamic density functional theory (DDFT). Such equations are challenging for standard PINN methods because they involve nonlinearities, nonlocal interaction terms, and an underlying gradient-flow structure, often leading to slow convergence and difficult optimization. We adapt the PINN methodology to DDFT gradient-flow equations and introduce two computational components: a modified Lorentzian activation function that behaves approximately linearly for small inputs and decays toward zero as the input magnitude increases, and a precomputed discrete operator for evaluating the nonlocal convolution term efficiently during training. The method is tested on four examples in one and two space dimensions. In the first example, the exact stationary solution is known, while in the remaining cases the neural-network approximations are validated against reference solutions computed using continuous and discontinuous Galerkin finite element discretizations. Accuracy and physical consistency are assessed through $L^1$, $L^2$, and $L^\infty$ errors, together with mass conservation and free-energy dissipation. The results show that the proposed activation function accelerates convergence relative to the standard $\tanh$ function, while the overall framework maintains good agreement with the reference solutions and captures the expected gradient-flow behaviour. These findings demonstrate the potential of the proposed PINN framework for solving nonlocal gradient-flow equations arising in DDFT.

math.NA↗

arXiv2026

Orientable Surfactants on Thin Liquid Films: A Dynamic Density-Functional Theory Approach

Thin liquid films are ubiquitous across many natural and engineering systems, including films which are laden with surface active molecules, i.e. surfactants. The presence of surfactants may have a destabilising effect on the film owing to their influence on surface tension, the so-called Marangoni effect, which in turn can induce flows in the film. Classical thin-film models for surfactant-laden films lead to paradigmatic gradient dynamics equations governing the film height and surfactant concentration and have been widely studied. However, in all these works, which are based on fluid dynamics or nonequilibrium thermodynamics, the shape of surfactants is neglected, and they have been treated as symmetric point-like particles. In general, this is a drastic oversimplification, as surfactants are amphiphilic with a polar head-tail structure. To account for this effect we use elements from the statistical mechanics of classical fluids, namely density-functional theory (DFT), and its dynamic extension (DDFT). Starting from DDFT and under the long-wave approximation, we derive the pertinent thin-film equations with the surfactants treated as polar uniaxial particles. These are equations which govern the film height, as well as the surfactant concentration and polarisation field. They preserve the gradient dynamics form by appropriately defining the free energy, which contains the usual interfacial contributions, as well as further contributions from the polarisation field. In doing so, we uncover a novel form of a generalised surface tension that is dependent on the surfactant polarisation as well as concentration, and show that it arises in a thermodynamically consistent way.

cond-mat.stat-mech↗

arXiv2024

Hydrodynamic density-functional theory for the moving contact-line problem reveals fluid structure and emergence of a spatially distinct pattern

Understanding the nanoscale effects controlling the dynamics of a contact line -- defined as the line formed at the junction of two fluid phases and a solid -- has been a longstanding problem in fluid mechanics pushing experimental and numerical methods to their limits. A major challenge is the multiscale nature of the problem, whereby nanoscale phenomena manifest themselves at the macroscale. To probe the nanoscale, not easily accessible to other methods, we propose a reductionist model that employs elements from statistical mechanics, namely dynamic-density-functional theory (DDFT), in a Navier-Stokes-like equation -- an approach we name hydrodynamic DDFT. The model is applied to an isothermal Lennard-Jones-fluid with no slip on a flat solid substrate. Our computations reveal fluid stratification with an oscillatory density structure close to the wall and the emergence of two distinct regions as the temperature increases: a region of compression on the vapor side of the liquid-vapour interface and an effective slip region of large shear on the liquid side. The compressive region spreads along the fluid interface at a lengthscale that increases faster than the width of the fluid interface with temperature, while the width of the slip region is bound by the oscillatory fluid density structure and is constrained to a few particle diameters from the wall. Both compressive and shear effects may offset contact line friction, while compression in particular has a disproportionately high effect on the speed of advancing contact lines at low temperatures.

physics.flu-dyn↗

arXiv2023

Physics-informed Bayesian inference of external potentials in classical density-functional theory

The swift progression of machine learning (ML) has not gone unnoticed in the realm of statistical mechanics. ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within DFT, the external potential accounts for the interaction of the many-particle system with an external field, thus, affecting the density distribution. In this context, we introduce a statistical-learning framework to infer the external potential exerted on a many-particle system. We combine a Bayesian inference approach with the classical DFT apparatus to reconstruct the external potential, yielding a probabilistic description of the external potential functional form with inherent uncertainty quantification. Our framework is exemplified with a grand-canonical one-dimensional particle ensemble with excluded volume interactions in a confined geometry. The required training dataset is generated using a Monte Carlo (MC) simulation where the external potential is applied to the grand-canonical ensemble. The resulting particle coordinates from the MC simulation are fed into the learning framework to uncover the external potential. This eventually allows us to compute the equilibrium density profile of the system by using the tools of DFT. Our approach benchmarks the inferred density against the exact one calculated through the DFT formulation with the true external potential. The proposed Bayesian procedure accurately infers the external potential and the density profile. We also highlight the external-potential uncertainty quantification conditioned on the amount of available simulated data. The seemingly simple case study introduced in this work might serve as a prototype for studying a wide variety of applications, including adsorption and capillarity.

cond-mat.stat-mech↗

arXiv2023

Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation

We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy. Our numerical framework is applicable to a variety of free-energy potentials, including Ginzburg-Landau and Flory-Huggins, to general wetting boundary conditions, and to degenerate mobilities. Its central thrust is the upwind methodology, which we combine with a semi-implicit formulation for the free-energy terms based on the classical convex-splitting approach. The extension of the schemes to an arbitrary number of dimensions is straightforward thanks to their dimensionally split nature, which allows to efficiently solve higher-dimensional problems with a simple parallelisation. The numerical schemes are validated and tested through a variety of examples, in different dimensions, and with various contact angles between droplets and substrates.

math.NA↗

arXiv2022

Machine learning memory kernels as closure for non-Markovian stochastic processes

Finding the dynamical law of observable quantities lies at the core of physics. Within the particular field of statistical mechanics, the generalized Langevin equation (GLE) comprises a general model for the evolution of observables covering a great deal of physical systems with many degrees of freedom and an inherently stochastic nature. Although formally exact, the GLE brings its own great challenges. It depends on the complete history of the observables under scrutiny, as well as the microscopic degrees of freedom, all of which are often inaccessible. We show that these drawbacks can be overcome by adopting elements of machine learning from empirical data, in particular coupling a multilayer perceptron (MLP) with the formal structure of the GLE and calibrating the MLP with the data. This yields a powerful computational tool capable of describing noisy complex systems beyond the realms of statistical mechanics. It is exemplified with a number of representative examples from different fields: from a single colloidal particle and particle chains in a thermal bath to climatology and finance, showing in all cases excellent agreement with the actual observable dynamics. The new framework offers an alternative perspective for the study of non-equilibrium processes opening also a new route for stochastic modelling.

cond-mat.stat-mech↗

arXiv2021

Physics-constrained Bayesian inference of state functions in classical density-functional theory

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that system? By combining non-parametric Bayesian inference with physically-motivated constraints, we develop an efficient learning algorithm which automates the construction of approximate free energy functionals. In contrast to optimisation-based machine learning approaches, which seek to minimise a cost function, the central idea of the proposed Bayesian inference is to propagate a set of prior assumptions through the model, derived from physical principles. The experimental data is used to probabilistically weigh the possible model predictions. This naturally leads to humanly interpretable algorithms with full uncertainty quantification of predictions. In our case, the output of the learning algorithm is a probability distribution over a family of free energy functionals, consistent with the observed particle data. We find that surprisingly small data samples contain sufficient information for inferring highly accurate analytic expressions of the underlying free energy functionals, making our algorithm highly data efficient. We consider excluded volume particle interactions, which are ubiquitous in nature, whilst being highly challenging for modelling in terms of free energy. To validate our approach we consider the paradigmatic case of one-dimensional fluid and develop inference algorithms for the canonical and grand-canonical statistical-mechanical ensembles. Extensions to higher-dimensional systems are conceptually straightforward, whilst standard coarse-graining techniques allow one to easily incorporate attractive interactions.

cond-mat.stat-mech↗

arXiv2021

Enhancement of damaged-image prediction through Cahn-Hilliard Image Inpainting

We assess the benefit of including an image inpainting filter before passing damaged images into a classification neural network. For this we employ a modified Cahn-Hilliard equation as an image inpainting filter, which is solved via a finite volume scheme with reduced computational cost and adequate properties for energy stability and boundedness. The benchmark dataset employed here is MNIST, which consists of binary images of handwritten digits and is a standard dataset to validate image-processing methodologies. We train a neural network based of dense layers with the training set of MNIST, and subsequently we contaminate the test set with damage of different types and intensities. We then compare the prediction accuracy of the neural network with and without applying the Cahn-Hilliard filter to the damaged images test. Our results quantify the significant improvement of damaged-image prediction due to applying the Cahn-Hilliard filter, which for specific damages can increase up to 50% and is in general advantageous for low to moderate damage.

cs.CV↗

arXiv2021

A Finite-Volume Method for Fluctuating Dynamical Density Functional Theory

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed scheme deals with general free-energy functionals, including, for instance, external fields or interaction potentials. This allows us to simulate a range of physical phenomena where thermal fluctuations play a crucial role, such as nucleation and other energy-barrier crossing transitions. A positivity-preserving algorithm for the density is derived based on a hybrid space discretization of the deterministic and the stochastic terms and different implicit and explicit time integrators. We show through numerous applications that not only our scheme is able to accurately reproduce the statistical properties (structure factor and correlations) of the physical system, but, because of the multiplicative noise, it allows us to simulate energy barrier crossing dynamics, which cannot be captured by mean-field approaches.

physics.comp-ph↗

arXiv2020

High-order well-balanced finite volume schemes for hydrodynamic equations with nonlocal free energy

We propose high-order well-balanced finite-volume schemes for a broad class of hydrodynamic systems with attractive-repulsive interaction forces and linear and nonlinear damping. Our schemes are suitable for free energies containing convolutions of an interaction potential with the density, which are essential for applications such as the Keller-Segel model, more general Euler-Poisson systems, or dynamic-density functional theory. Our schemes are also equipped with a nonnegative-density reconstruction which allows for vacuum regions during the simulation. We provide several prototypical examples from relevant applications highlighting the benefit of our algorithms elucidate also some of our analytical results.

math.NA↗

arXiv2020

Well-balanced finite volume schemes for hydrodynamic equations with general free energy

Well balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The natural Liapunov functional of the system, given by its free energy, allows for a characterization of the stationary states by its variation. An analog property at the discrete level enables us to preserve stationary states at machine precision while keeping the dissipation of the discrete free energy. These schemes allow for analysing accurately the stability properties of stationary states in challeging problems such as: phase transitions in collective behavior, generalized Euler-Poisson systems in chemotaxis and astrophysics, and models in dynamic density functional theories; having done a careful validation in a battery of relevant test cases.

math.NA↗

arXiv2019

Dynamics of the Desai-Zwanzig model in multi-well and random energy landscapes

We analyze a variant of the Desai-Zwanzig model [J. Stat. Phys. {\bf 19}1-24 (1978)]. In particular, we study stationary states of the mean field limit for a system of weakly interacting diffusions moving in a multi-well potential energy landscape, coupled via a Curie-Weiss type (quadratic) interaction potential. The location and depth of the local minima of the potential are either deterministic or random. We characterize the structure and nature of bifurcations and phase transitions for this system, by means of extensive numerical simulations and of analytical calculations for an explicitly solvable model. Our numerical experiments are based on Monte Carlo simulations, the numerical solution of the time-dependent nonlinear Fokker-Planck (McKean-Vlasov equation), the minimization of the free energy functional and a continuation algorithm for the stationary solutions.

cond-mat.stat-mech↗

arXiv2019

Instability, rupture and fluctuations in thin liquid films: Theory and computations

Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. In this work we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. Following a brief review of the derivation, we scrutinise the behaviour of the equation in the limit of perfectly correlated noise along the wall-normal direction. The stochastic thin-film equation is also simulated by adopting a numerical scheme based on a spectral collocation method. The scheme allows us to explore the fluctuating dynamics of the thin film and the behaviour of its free energy in the vicinity of rupture. Finally, we also study the effect of the noise intensity on the rupture time, which is in agreement with previous works.

physics.flu-dyn↗

arXiv2018

The pressure tensor across a liquid-vapour interface

Inhomogeneous fluids exhibit physical properties that are neither uniform nor isotropic. The pressure tensor is a case in point, key to the mechanical description of the interfacial region. Kirkwood and Buff, and later Irving and Kirkwood, obtained a formal treatment based on the analysis of the pressure across a planar surface [J.G. Kirkwood and F.P. Buff, J. Chem. Phys., 17(3), (1949), J.H. Irving and J.G. Kirkwood, J. Chem. Phys. 18, 817 (1950)]. We propose a generalisation of Irving and Kirkwood's argument to fluctuating, non-planar surfaces and obtain an expression for the pressure tensor that is not smeared by thermal fluctuations at the molecular scale and corresponding capillary waves [F.P. Buff, R.A. Lovett, and F.H. Stillinger, Jr., Phys. Rev. Lett. 15, 621 (1965)]. We observe the emergence of surface tension, defined as an excess tangential stress, acting exactly across the dividing surface at the sharpest molecular resolution. The new statistical mechanical expressions extend current treatments to fluctuating inhomogeneous systems far from equilibrium.

cond-mat.stat-mech↗

arXiv2017

Discrete self-similarity in interfacial hydrodynamics and the formation of iterated structures

The formation of iterated structures, such as satellite and sub-satellite drops, filaments and bubbles, is a common feature in interfacial hydrodynamics. Here we undertake a computational and theoretical study of their origin in the case of thin films of viscous fluids that are destabilized by long-range molecular or other forces. We demonstrate that iterated structures appear as a consequence of discrete self-similarity, where certain patterns repeat themselves, subject to rescaling, periodically in a logarithmic time scale. The result is an infinite sequence of ridges and filaments with similarity properties. The character of these discretely self-similar solutions as the result of a Hopf bifurcation from ordinarily self-similar solutions is also described.

physics.flu-dyn↗