arXiv subjects

Giovanni Russo

Publications and source records attributed to Giovanni Russo.

At least 37 records · Page 2Linked to original sources

arXiv2026

An efficient implicit scheme for the multimaterial Euler equations in Lagrangian coordinates

Stratified fluids composed of a sequence of alternate layers show interesting macroscopic properties, which may be quite different from those of the individual constituent fluids. On a macroscopic scale, such systems can be considered a sort of fluid metamaterial. In many cases each fluid layer can be described by Euler equations following the stiffened gas equation of state. The computation of detailed numerical solutions of such stratified material poses several challenges, first and foremost the issue of artificial smearing of material parameters across interface boundaries. Lagrangian schemes completely eliminate this issue, but at the cost of rather stringent time step restrictions. In this work we introduce an implicit numerical method for the multimaterial Euler equations in Lagrangian coordinates. The implicit discretization is aimed at bypassing the prohibitive time step restrictions present in flows with stratified media, where one of the materials is particularly dense, or rigid (or both). This is the case for flows of water-air mixtures, air-granular media, or similar high density ratio systems. We will present the novel discretisation approach, which makes extensive use of the remarkable structure of the governing equations in Lagrangian coordinates to find the solution by means of a single implicit discrete wave equation for the pressure field, yielding a symmetric positive definite structure and thus a particularly efficient algorithm. Additionally, we will introduce simple filtering strategies for counteracting the emergence of pressure or density oscillations typically encountered in multimaterial flows, and will present results concerning the robustness, accuracy, and performance of the proposed method, including applications to stratified media with high density and stiffness ratios.

math.NA↗

arXiv2025

Distributionally Robust Free Energy Principle for Decision-Making

Despite their groundbreaking performance, autonomous agents can misbehave when training and environmental conditions become inconsistent, with minor mismatches leading to undesirable behaviors or even catastrophic failures. Robustness towards these training-environment ambiguities is a core requirement for intelligent agents and its fulfillment is a long-standing challenge towards their real-world deployments. Here, we introduce a Distributionally Robust Free Energy model (DR-FREE) that instills this core property by design. Combining a robust extension of the free energy principle with a resolution engine, DR-FREE wires robustness into the agent decision-making mechanisms. Across benchmark experiments, DR-FREE enables the agents to complete the task even when, in contrast, state-of-the-art models fail. This milestone may inspire both deployments in multi-agent settings and, at a perhaps deeper level, the quest for an explanation of how natural agents -- with little or no training -- survive in capricious environments.

cs.AI↗

arXiv2025

A bioreactor-based architecture for in vivo model-based and sim-to-real learning control of microbial consortium composition

Microbial consortia offer significant biotechnological advantages over monocultures for bioproduction. However, industrial deployment is hampered by the lack of scalable architectures to ensure stable coexistence between populations. Existing strategies rely on genetic modifications, which impose metabolic load, or environmental changes, which can reduce production. We present a versatile control architecture to regulate density and composition of a two-strain consortium without genetic engineering or drastic environmental changes. Our bioreactor-based control architecture comprises a mixing chamber where both strains are co-cultured and a reservoir sustaining the slower-growing strain. For both chambers we develop model-based and sim-to-real learning controllers. The control architecture is then validated in vivo on a two-strain Escherichia coli consortium, achieving precise and robust regulation of consortium density and composition, including tracking of time-varying references and recovery from perturbations.

eess.SY↗

arXiv2025

A quantitative comparison of high-order asymptotic-preserving and asymptotically-accurate IMEX methods for the Euler equations with non-ideal gases

We present a quantitative comparison between two different Implicit-Explicit Runge-Kutta (IMEX-RK) approaches for the Euler equations of gas dynamics, specifically tailored for the low Mach limit. In this regime, a classical IMEX-RK approach involves an implicit coupling between the momentum and energy balance so as to avoid the acoustic CFL restriction, while the density can be treated in a fully explicit fashion. This approach leads to a mildly nonlinear equation for the pressure, which can be solved according to a fixed point procedure. An alternative strategy consists of employing a semi-implicit temporal integrator based on IMEX-RK methods (SI-IMEX-RK). The stiff dependence is carefully analyzed, so as to avoid the solution of a nonlinear equation for the pressure also for equations of state (EOS) of non-ideal gases. The spatial discretization is based on a Discontinuous Galerkin (DG) method, which naturally allows high-order accuracy. The asymptotic-preserving (AP) and the asymptotically-accurate (AA) properties of the two approaches are assessed on a number of classical benchmarks for ideal gases and on their extension to non-ideal gases.

math.NA↗

arXiv2025

Free-Gate: Planning, Control And Policy Composition via Free Energy Gating

We consider the problem of optimally composing a set of primitives to tackle planning and control tasks. To address this problem, we introduce a free energy computational model for planning and control via policy composition: Free-Gate. Within Free-Gate, control primitives are combined via a gating mechanism that minimizes variational free energy. This composition problem is formulated as a finite-horizon optimal control problem, which we prove remains convex even when the cost is not convex in states/actions and the environment is nonlinear, stochastic and non-stationary. We develop an algorithm that computes the optimal primitives composition and demonstrate its effectiveness via in-silico and hardware experiments on an application involving robot navigation in an environment with obstacles. The experiments highlight that Free-Gate enables the robot to navigate to the destination despite only having available simple motor primitives that, individually, could not fulfill the task.

math.OC↗

arXiv2025

A third-order finite volume semi-implicit method for the Shallow Water-Exner model

In this work, third-order semi-implicit schemes on staggered meshes for the shallow water and Saint-Venant-Exner systems are presented. They are based on a third-order extension of the technique introduced in Cassulli \& Cheng [1]. The stability conditions for these schemes depend on the velocity and not on the celerity, allowing us to reduce computational efforts, especially in subcritical flow simulations, which is the regime we are mainly interested in. The main novelty consists in the third-order approximation of the pressure gradient term in the momentum equation through appropriate polynomial reconstructions. Concretely, CWENO conservative reconstruction is considered for the water thickness $h$ and a centered fourth-degree polynomial is adopted interpolating the cell averages of the free surface $η$. For time discretization, a third-order IMEX scheme is applied. In addition, a novel time-dependent semi-analytical solution for Saint-Venant-Exner system is introduced and compared with the numerical ones. Several tests are performed, including accuracy tests showing third-order accuracy, well-balance tests, and simulations of slow bedload processes for large time.

math.NA↗

arXiv2025

Similarity Matching Networks: Hebbian Learning and Convergence Over Multiple Time Scales

A recent breakthrough in biologically-plausible normative frameworks for dimensionality reduction is based upon the similarity matching cost function and the low-rank matrix approximation problem. Despite clear biological interpretation, successful application in several domains, and experimental validation, a formal complete convergence analysis remains elusive. Building on this framework, we consider and analyze a continuous-time neural network, the \emph{similarity matching network}, for principal subspace projection. Derived from a min-max-min objective, this biologically-plausible network consists of three coupled dynamics evolving at different time scales: neural dynamics, lateral synaptic dynamics, and feedforward synaptic dynamics at the fast, intermediate, and slow time scales, respectively. The feedforward and lateral synaptic dynamics consist of Hebbian and anti-Hebbian learning rules, respectively. By leveraging a multilevel optimization framework, we prove convergence of the dynamics in the offline setting. Specifically, at the first level (fast time scale), we show strong convexity of the cost function and global exponential convergence of the corresponding gradient-flow dynamics. At the second level (intermediate time scale), we prove strong concavity of the cost function and exponential convergence of the corresponding gradient-flow dynamics within the space of positive definite matrices. At the third and final level (slow time scale), we study a non-convex and non-smooth cost function, provide explicit expressions for its global minima, and prove almost sure convergence of the corresponding gradient-flow dynamics to the global minima. These results rely on two empirically motivated conjectures that are supported by thorough numerical experiments. Finally, we validate the effectiveness of our approach via a numerical example.

q-bio.NC↗

arXiv2025

A dispersive effective equation for transverse propagation of planar shallow water waves over periodic bathymetry

We study the behavior of shallow water waves propagating over bathymetry that varies periodically in one direction and is constant in the other. Plane waves traveling along the constant direction are known to evolve into solitary waves, due to an effective dispersion. We apply multiple-scale perturbation theory to derive an effective constant-coefficient system of equations, showing that the transversely-averaged wave approximately satisfies a Boussinesq-type equation, while the lateral variation in the wave is related to certain integral functions of the bathymetry. Thus the homogenized equations not only accurately describe these waves but also predict their full two-dimensional shape in some detail. Numerical experiments confirm the good agreement between the effective equations and the variable-bathymetry shallow water equations.

math.AP↗

arXiv2025

Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations -- with and without Manning friction -- or Euler equations of gas dynamics with gravity effects.

math.NA↗

arXiv2025

Topics in representation theory and Riemannian geometry

These are notes for a Ph.D.\ course I held at SISSA, Trieste, in the Winter 2025. We review well-known topics in Riemannian geometry where Lie groups play a fundamental role. Part of the theory of compact connected Lie groups, their invariants, and representations is discussed, with particular emphasis on low dimensional examples. We go through a number of applications in Riemannian geometry, in particular the classification of Riemannian holonomy groups, and the first construction of exceptional holonomy metrics. Some more recent advances in the field of Riemannian geometry with symmetries are mentioned.

math.DG↗

arXiv2025

DR-PETS: Learning-Based Control With Planning in Adversarial Environments

Ensuring robustness against epistemic, possibly adversarial, perturbations is essential for reliable real-world decision-making. While the Probabilistic Ensembles with Trajectory Sampling (PETS) algorithm inherently handles uncertainty via ensemble-based probabilistic models, it lacks guarantees against structured adversarial or worst-case uncertainty distributions. To address this, we propose DR-PETS, a distributionally robust extension of PETS that certifies robustness against adversarial perturbations. We formalize uncertainty via a p-Wasserstein ambiguity set, enabling worst-case-aware planning through a min-max optimization framework. While PETS passively accounts for stochasticity, DR-PETS actively optimizes robustness via a tractable convex approximation integrated into PETS planning loop. Experiments on pendulum stabilization and cart-pole balancing show that DR-PETS certifies robustness against adversarial parameter perturbations, achieving consistent performance in worst-case scenarios where PETS deteriorates.

cs.LG↗

arXiv2025

A conservative semi-Lagrangian scheme for the ellipsoidal BGK model of the Boltzmann equation

In this paper, we propose a high order conservative semi-Lagrangian scheme (SL) for the ellipsoidal BGK model of the Boltzmann transport equation. To avoid the time step restriction induced by the convection term, we adopt the semi-Lagrangian approach. For treating the nonlinear stiff relaxation operator with small Knudsen number, we employ high order $L$-stable diagonally implicit Runge-Kutta time discretization or backward difference formula. The proposed implicit schemes are designed to update solutions explicitly without resorting to any Newton solver. We present several numerical tests to demonstrate the accuracy and efficiency of the proposed methods. These methods allow us to obtain accurate approximations of the solutions to the Navier-Stokes equations or the Boltzmann equation for moderate or relatively large Knudsen numbers, respectively.

math.NA↗

arXiv2025

A multiscale model for weakly nonlinear shallow water waves over periodic bathymetry

We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical experiments suggest a different behavior in the presence of periodic bathymetry. Starting from the first-order variable-coefficient hyperbolic system, we apply a multiple-scale perturbation approach in order to derive a system of constant-coefficient high-order partial differential equations whose solution approximates that of the original system. The high-order system turns out to be dispersive and exhibits solitary-wave formation, in close agreement with direct numerical simulations of the original system. We show that the constant-coefficient homogenized system can be used to study the properties of solitary waves and to conduct efficient numerical simulations.

math.AP↗

arXiv2025

Approximate Taylor methods for ODEs

A new method for the numerical solution of ODEs is presented. This approach is based on an approximate formulation of the Taylor methods that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their derivatives, are needed, just as in classical Runge-Kutta schemes. Compared to Runge-Kutta methods, the number of function evaluations to achieve a given order is higher, however with the present procedure it is much easier to produce arbitrary high-order schemes, which may be important in some applications. In many cases the new approach leads to an asymptotically lower computational cost when compared to the Taylor expansion based on exact derivatives. The numerical results that are obtained with our proposal are satisfactory and show that this approximate approach can attain results as good as the exact Taylor procedure with less implementation and computational effort.

math.NA↗

arXiv2025

Time-Varying Convex Optimization: A Contraction and Equilibrium Tracking Approach

In this article, we provide a novel and broadly-applicable contraction-theoretic approach to continuous-time time-varying convex optimization. For any parameter-dependent contracting dynamics, we show that the tracking error is asymptotically proportional to the rate of change of the parameter and that the proportionality constant is upper bounded by Lipschitz constant in which the parameter appears divided by the contraction rate of the dynamics squared. We additionally establish that augmenting any parameter-dependent contracting dynamics with a feedforward prediction term ensures that the tracking error vanishes exponentially quickly. To apply these results to time-varying convex optimization, we establish the strong infinitesimal contractivity of dynamics solving three canonical problems: monotone inclusions, linear equality-constrained problems, and composite minimization problems. For each case, we derive the sharpest-known contraction rates and provide explicit bounds on the tracking error between solution trajectories and minimizing trajectories. We validate our theoretical results on two numerical examples and on an application to control barrier function-based controller design that involves real hardware.

math.OC↗

arXiv2024

A nodal ghost method based on variational formulation and regular square grid for elliptic problems on arbitrary domains in two space dimensions

This paper focuses on the numerical solution of elliptic partial differential equations (PDEs) with Dirichlet and mixed boundary conditions, specifically addressing the challenges arising from irregular domains. Both finite element method (FEM) and finite difference method (FDM), face difficulties in dealing with arbitrary domains. The paper introduces a novel nodal symmetric ghost {method based on a variational formulation}, which combines the advantages of FEM and FDM. The method employs bilinear finite elements on a structured mesh and provides a detailed implementation description. A rigorous a priori convergence rate analysis is also presented. The convergence rates are validated with many numerical experiments, in both one and two space dimensions.

math.NA↗

arXiv2024

Kinetic derivation of a compressible Leslie--Ericksen equation for rarified calamitic gases

Nematic ordering describes the phenomenon where anisotropic molecules tend to locally align, like matches in a matchbox. This ordering can arise in solids (as nematic elastomers), liquids (as liquid crystals), and in gases. In the 1940s, Onsager described how nematic ordering can arise in dilute colloidal suspensions from the molecular point of view. However, the kinetic theory of nonspherical molecules has not, thus far, accounted for phenomena relating to the presence of nematic ordering. In this work we develop a kinetic theory for the behavior of rarified calamitic (rodlike) gases in the presence of nematic ordering. Building on previous work by Curtiss, we derive from kinetic theory the rate of work hypothesis that forms the starting point for Leslie--Ericksen theory. We incorporate ideas from the variational theory of nematic liquid crystals to create a moment closure that preserves the coupling between the laws of linear and angular momentum. The coupling between these laws is a key feature of our theory, in contrast to the kinetic theory proposed by {Curtiss \& Dahler}, where the couple stress tensor is assumed to be zero. This coupling allows the characterization of anisotropic phenomena arising from the nematic ordering. Furthermore, the theory leads to an energy functional that is a compressible variant of the classical Oseen--Frank energy (with a pressure-dependent Frank constant) and to a compressible analogue of the Leslie--Ericksen equations. The emergence of compressible aspects in the theory for nematic fluids enhances our understanding of these complex systems.

math-ph↗

arXiv2024

A pair-based approximation for simplicial contagion

Higher-order interactions play an important role in complex contagion processes. Mean-field approximations have been used to characterize the onset of spreading in the presence of group interactions. However, individual-based mean-field models are unable to capture correlations between different subsets of nodes, which can significantly influence the dynamics of a contagion process. In this paper, we introduce a pair-based mean-field approximation that allows to study the dynamics of a SIS model on simplicial complexes by taking into account correlations at the level of pairs of nodes. %by taking into account dynamical correlations emerging in groups of nodes. Compared to individual-based mean-field approaches, the proposed approximation yields more accurate predictions of the dynamics of contagion processes on simplicial complexes. Specifically, the pair-based mean-field approximation provides higher accuracy in predicting the extent of the region of bistability, the type of transition from disease-free to endemic state, and the average time evolution of the fraction of infected individuals. Crucially, the pair-based approximation correctly predicts that the onset of the epidemic outbreak in simplicial complexes depends on the strength of higher-order interactions. Overall, our findings highlight the importance of accounting for pair correlations when investigating contagion processes in the presence of higher-order interactions.

physics.soc-ph↗