arXiv subjects

Vakhtang Putkaradze

Publications and source records attributed to Vakhtang Putkaradze.

At least 19 recordsLinked to original sources

arXiv2026

Estimation of Spacecraft Inertia Tensor Using Attitude-Only Data from Torque-Free Motion

We present an attitude-only framework for estimating a spacecraft's normalized inertia tensor from torque-free rotational motion. Our method supports both continuous single-arc observations and the joint use of multiple short torque-free arcs, while requiring neither gyroscope measurements nor known control torques. A Karush-Kuhn-Tucker formulation provides a fast linear initialization, which is refined by nonlinear shooting using the exact Jacobi-elliptic solution of Euler's equations and a Magnus-expansion quaternion map. Under controlled attitude noise, tests using a single 500-second arc reduced inertia-tensor error by approximately one order of magnitude relative to an Extended Kalman Filter initialized from the same estimate, while requiring nearly two orders of magnitude less computation. Joint estimation from three 100-second arcs provided a similar improvement in accuracy and remained more than one order of magnitude faster. Photorealistic proximity-operations simulations further evaluated both strategies using monocular image-derived attitudes. The 2000-second single-arc cases achieved sub-thousandth median inertia-tensor error and supported 10-hour attitude predictions with single-digit-degree median error. In three-arc cases using 30-300 seconds per arc, our method consistently outperformed the EKF refinement, with performance governed by rotational excitation and temporal sampling.

cs.RO↗

arXiv2026

The Neural Division of Labor: Biologically-Inspired Modular Architectures for Robust Neuromorphic Computing

Biological neural systems achieve high efficiency and robustness through compartmentalized architectures. In contrast, modern artificial neural networks rely on globally entangled structures, which obscure decision logic and suffer from catastrophic forgetting. Here, we report a Decomposable Spiking Neural Network (D-SNN) that eliminates global synaptic entanglement by structurally isolating classification pathways into independent experts. Optimized via a bio-inspired push-pull loss function, the D-SNN achieves competitive accuracies on MNIST, Fashion-MNIST, and CIFAR-10/100 benchmarks. This modular approach matches the performance of fully dense networks while utilizing an order of magnitude fewer parameters. In addition, our networks operate with up to several orders of magnitude lower firing rates and fewer synaptic operations. Furthermore, physically severing connections between experts provides inherent protection against catastrophic forgetting during sequential learning. Crucially, these isolated pathways generate auditable neural signals, increasing decision transparency. This biomimetic, verifiable architecture establishes an efficient foundation for deploying deterministic neuromorphic intelligence in resource-constrained edge environments.

cs.LG↗

arXiv2026

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics

Structure-preserving neural networks are essential for the long-term prediction of Hamiltonian systems from data. Many important Hamiltonian systems in mechanics and control admit symmetry reduction to Lie--Poisson systems, including rigid bodies, underwater vehicles, fluids, plasmas, and optimal control problems. A fundamental challenge in learning such systems is that their dynamics evolve in momentum variables that are typically unobservable, while available data consist only of observable quantities such as configurations and velocities. In optimal control applications, the situation is further complicated because the latent variables contain unobservable co-states and the Hamiltonian may be degenerate, preventing the existence of a corresponding Lagrangian and rendering the encoder-decoder approaches inapplicable. We introduce Latent Lie--Poisson Neural Networks (LLPNNs), a structure-preserving framework for learning Lie--Poisson dynamics directly from observable data. The proposed approach exploits three geometric ingredients: (i) learning either a Hamiltonian decoder or a pseudo-Lagrangian encoder on the active variables, (ii) constructing latent trajectories through a universal Noether invariant arising from Lie--Poisson symmetry reduction, and (iii) reconstructing observable and latent dynamics through Lie--Poisson flows combined with Magnus-based Lie-group updates. The resulting method preserves the geometric structure and is applicable to both regular and degenerate Hamiltonian systems. We demonstrate the method on three examples: a generalized rigid body on SO(3), Kirchhoff's underwater vehicle on SE(3), and an optimal-control problem for interacting vehicles on $SE(2)^N$. Numerical experiments show excellent long-term predictive accuracy, strong robustness to noise, and competitive performance using only modest datasets and lightweight neural-network architectures.

cs.LG↗

arXiv2026

Variational Neural Networks for Observable Thermodynamics (V-NOTS)

Much attention has recently been devoted to data-based computing of evolution of physical systems. In such approaches, information about data points from past trajectories in phase space is used to reconstruct the equations of motion and to predict future solutions that have not been observed before. However, in many cases, the available data does not correspond to the variables that define the system's phase space. We focus our attention on the important example of dissipative dynamical systems. In that case, the phase space consists of coordinates, momenta and entropies; however, the momenta and entropies cannot, in general, be observed directly. To address this difficulty, we develop an efficient data-based computing framework based exclusively on observable variables, by constructing a novel approach based on the thermodynamic Lagrangian, and constructing neural networks that respect the thermodynamics and guarantees the non-decreasing entropy evolution. We show that our network can provide an efficient description of phase space evolution based on a limited number of data points and a relatively small number of parameters in the system.

cs.LG↗

arXiv2026

Structure-preserving learning and prediction in optimal control of collective motion

Wide-spread adoption of unmanned vehicle technologies requires the ability to predict the motion of the combined vehicle operation from observations. While the general prediction of such motion for an arbitrary control mechanism is difficult, for a particular choice of control, the dynamics reduces to the Lie-Poisson equations [33,34]. Our goal is to learn the phase-space dynamics and predict the motion solely from observations, without any knowledge of the control Hamiltonian or the nature of interaction between vehicles. To achieve that goal, we propose the Control Optimal Lie-Poisson Neural Networks (CO-LPNets) for learning and predicting the dynamics of the system from data. Our methods learn the mapping of the phase space through the composition of Poisson maps, which are obtained as flows from Hamiltonians that could be integrated explicitly. CO-LPNets preserve the Poisson bracket and thus preserve Casimirs to machine precision. We discuss the completeness of the derived neural networks and their efficiency in approximating the dynamics. To illustrate the power of the method, we apply these techniques to systems of $N=3$ particles evolving on ${\rm SO}(3)$ group, which describe coupled rigid bodies rotating about their center of mass, and ${\rm SE}(3)$ group, applicable to the movement of unmanned air and water vehicles. Numerical results demonstrate that CO-LPNets learn the dynamics in phase space from data points and reproduce trajectories, with good accuracy, over hundreds of time steps. The method uses a limited number of points ($\sim200$/dimension) and parameters ($\sim 1000$ in our case), demonstrating potential for practical applications and edge deployment.

cs.LG↗

arXiv2024

CLPNets: Coupled Lie-Poisson Neural Networks for Multi-Part Hamiltonian Systems with Symmetries

To accurately compute data-based prediction of Hamiltonian systems, especially the long-term evolution of such systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a case that is particularly challenging for data-based methods: systems with interacting parts that do not reduce to pure momentum evolution. Such systems are essential in scientific computations. For example, any discretization of a continuum elastic rod can be viewed as interacting elements that can move and rotate in space, with each discrete element moving on the group of rotations and translations $SE(3)$. We develop a novel method of data-based computation and complete phase space learning of such systems. We follow the original framework of \emph{SympNets} (Jin et al, 2020) building the neural network from canonical phase space mappings, and transformations that preserve the Lie-Poisson structure (\emph{LPNets}) as in (Eldred et al, 2024). We derive a novel system of mappings that are built into neural networks for coupled systems. We call such networks Coupled Lie-Poisson Neural Networks, or \emph{CLPNets}. We consider increasingly complex examples for the applications of CLPNets: rotation of two rigid bodies about a common axis, the free rotation of two rigid bodies, and finally the evolution of two connected and interacting $SE(3)$ components. Our method preserves all Casimir invariants of each system to machine precision, irrespective of the quality of the training data, and preserves energy to high accuracy. Our method also shows good resistance to the curse of dimensionality, requiring only a few thousand data points for all cases studied, with the effective dimension varying from three to eighteen. Additionally, the method is highly economical in memory requirements, requiring only about 200 parameters for the most complex case considered.

cs.LG↗

arXiv2024

The Dictator Dilemma: The Distortion of Information Flow in Autocratic Regimes and Its Consequences

Humans have been arguing about the benefits of dictatorial versus democratic regimes for millennia. Despite drastic differences between the dictatorships in the world, one of the key common features is the \emph{Dictator's Dilemma} as defined by Wintrobe [1]: a dictator will never know the true state of affairs in his country and is perpetually presented distorted information, thus having difficulties in making the right governing decisions. The dictator's dilemma is essential to most autocratic regimes and is one of the key features in the literature on the subject. Yet, no quantitative theory of how the distortion of information develops from the initial state has been developed up to date. I present a model of the appearance and evolution of such information distortion, with subsequent degradation of control by the dictator. The model is based on the following fundamental and general premises: a) the dictator governs aiming to follow the desired trajectory of development based only on the information from the advisors; b) the deception from the advisors cannot decrease in time; and c) the deception change depends on the difficulties the country encounters. The model shows effective control in the short term (a few months to a year), followed by instability leading to the country's gradual deterioration of the state over many years. I derive some universal parameters applicable to all dictators and show that advisors' deception increases parallel with the decline of the control. In contrast, the dictator thinks the government is doing a reasonable, but not perfect, job. Finally, I present a match of our model to the historical data of grain production in the Soviet Union in 1928-1940.

nlin.AO↗

arXiv2023

Lie-Poisson Neural Networks (LPNets): Data-Based Computing of Hamiltonian Systems with Symmetries

An accurate data-based prediction of the long-term evolution of Hamiltonian systems requires a network that preserves the appropriate structure under each time step. Every Hamiltonian system contains two essential ingredients: the Poisson bracket and the Hamiltonian. Hamiltonian systems with symmetries, whose paradigm examples are the Lie-Poisson systems, have been shown to describe a broad category of physical phenomena, from satellite motion to underwater vehicles, fluids, geophysical applications, complex fluids, and plasma physics. The Poisson bracket in these systems comes from the symmetries, while the Hamiltonian comes from the underlying physics. We view the symmetry of the system as primary, hence the Lie-Poisson bracket is known exactly, whereas the Hamiltonian is regarded as coming from physics and is considered not known, or known approximately. Using this approach, we develop a network based on transformations that exactly preserve the Poisson bracket and the special functions of the Lie-Poisson systems (Casimirs) to machine precision. We present two flavors of such systems: one, where the parameters of transformations are computed from data using a dense neural network (LPNets), and another, where the composition of transformations is used as building blocks (G-LPNets). We also show how to adapt these methods to a larger class of Poisson brackets. We apply the resulting methods to several examples, such as rigid body (satellite) motion, underwater vehicles, a particle in a magnetic field, and others. The methods developed in this paper are important for the construction of accurate data-based methods for simulating the long-term dynamics of physical systems.

cs.LG↗

arXiv2023

Thermodynamically consistent variational theory of porous media with a breaking component

If a porous media is being damaged by excessive stress, the elastic matrix at every infinitesimal volume separates into a 'solid' and a 'broken' component. The 'solid' part is the one that is capable of transferring stress, whereas the 'broken' part is advecting passively and is not able to transfer the stress. In previous works, damage mechanics was addressed by introducing the damage parameter affecting the elastic properties of the material. In this work, we take a more microscopic point of view, by considering the transition from the 'solid' part, which can transfer mechanical stress, to the 'broken' part, which consists of microscopic solid particles and does not transfer mechanical stress. Based on this approach, we develop a thermodynamically consistent dynamical theory for porous media including the transfer between the 'broken' and 'solid' components, by using a variational principle recently proposed in thermodynamics. This setting allows us to derive an explicit formula for the breaking rate, i.e., the transition from the 'solid' to the 'broken' phase, dependent on the Gibbs' free energy of each phase. Using that expression, we derive a reduced variational model for material breaking under one-dimensional deformations. We show that the material is destroyed in finite time, and that the number of 'solid' strands vanishing at the singularity follows a power law. We also discuss connections with existing experiments on material breaking and extensions to multi-phase porous media.

physics.flu-dyn↗

arXiv2021

Trajectory tracing in figure skating

In this work, we model the movement of a figure skater gliding on ice by the Chaplygin sleigh, a classic pedagogical example of a nonholonomic mechanical system. The Chaplygin sleigh is controlled by a movable added mass, modeling the movable center of mass of the figure skater. The position and velocity of the added mass act as controls that can be used to steer the skater in order to produce prescribed patterns. For any piecewise smooth prescribed curve, this model can be used to determine the controls needed to reproduce that curve by approximating the curve with circular arcs. Tracing of the circular arcs is exact in our control procedure, so the accuracy of the method depends solely on the accuracy of approximation of a trajectory by circular arcs. To reproduce the individual elements of a pattern, we employ an optimization algorithm. We conclude by reproducing a classical "double flower" figure skating pattern and compute the resulting controls.

math.OC↗

arXiv2021

Variational geometric approach to the thermodynamics of porous media

Many applications of porous media research involves high pressures and, correspondingly, exchange of thermal energy between the fluid and the matrix. While the system is relatively well understood for the case of non-moving porous media, the situation when the elastic matrix can move and deform, is much more complex. In this paper we derive the equations of motion for the dynamics of a deformable porous media which includes the effects of friction forces, stresses, and heat exchanges between the media, by using the new methodology of variational approach to thermodynamics. This theory extends the recently developed variational derivation of the mechanics of deformable porous media to include thermodynamic processes and can easily include incompressibility constraints. The model for the combined fluid-matrix system, written in the spatial frame, is developed by introducing mechanical and additional variables describing the thermal energy part of the system, writing the action principle for the system, and using a nonlinear, nonholonomic constraint on the system deduced from the second law of thermodynamics. The resulting equations give us the general version of possible friction forces incorporating thermodynamics, Darcy-like forces and friction forces similar to those used in the Navier-Stokes equations. The equations of motion are valid for arbitrary dependence of the kinetic and potential energies on the state variables. The results of our work are relevant for geophysical applications, industrial applications involving high pressures and temperatures, food processing industry, and other situations when both thermodynamics and mechanical considerations are important.

physics.flu-dyn↗

arXiv2021

Actively deforming porous media in an incompressible fluid: a variational approach

Many parts of biological organisms are comprised of deformable porous media. The biological media is both pliable enough to deform in response to an outside force and can deform by itself using the work of an embedded muscle. For example, the recent work (Ludeman et al., 2014) has demonstrated interesting 'sneezing' dynamics of a freshwater sponge, when the sponge contracts and expands to clear itself from surrounding polluted water. We derive the equations of motion for the dynamics of such an active porous media (i.e., a deformable porous media that is capable of applying a force to itself with internal muscles), filled with an incompressible fluid. These equations of motion extend the earlier derived equation for a passive porous media filled with an incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the elastic matrix, and the kinetic energy of the fluid, coupled through the constraint of incompressibility. We then proceed to extend this theory by computing the case when both the active porous media and the fluid are incompressible, with the porous media still being deformable, which is often the case for biological applications. For the particular case of a uniform initial state, we rewrite the equations of motion in terms of two coupled telegraph-like equations for the material (Lagrangian) particles expressed in the Eulerian frame of reference, particularly suitable for numerical simulations, formulated for both the compressible media/incompressible fluid case and the doubly incompressible case. We derive interesting conservation laws for the motion, perform numerical simulations in both cases and show the possibility of self-propulsion of a biological organism due to particular running wave-like application of the muscle stress.

physics.flu-dyn↗

arXiv2020

Geometric variational approach to the dynamics of porous media filled with incompressible fluid

We derive the equations of motion for the dynamics of a porous media filled with an incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the elastic matrix, and the kinetic energy of the fluid, coupled through the constraint of incompressibility. As an illustration of the method, the equations of motion for both the elastic matrix and the fluid are derived in the spatial (Eulerian) frame. Such an approach is of relevance e.g. for biological problems, such as sponges in water, where the elastic porous media is highly flexible and the motion of the fluid has a 'primary' role in the motion of the whole system. We then analyze the linearized equations of motion describing the propagation of waves through the media. In particular, we derive the propagation of S-waves and P-waves in an isotropic media. We also analyze the stability criteria for the wave equations and show that they are equivalent to the physicality conditions of the elastic matrix. Finally, we show that the celebrated Biot's equations for waves in porous media are obtained for certain values of parameters in our models.

physics.flu-dyn↗

arXiv2020

Numerical Simulations of a Rolling Ball Robot Actuated by Internal Point Masses

The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. The controlled equations of motion are solved numerically using a predictor-corrector continuation method, starting from an initial solution obtained via a direct method, to realize trajectory tracking and obstacle avoidance maneuvers.

math.OC↗

arXiv2020

On the Optimal Control of a Rolling Ball Robot Actuated by Internal Point Masses

The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. Application of the variational Pontryagin's minimum principle yields the ball's controlled equations of motion, a solution of which obeys the ball's uncontrolled equations of motion, satisfies prescribed initial and final conditions, and minimizes a prescribed performance index.

math.OC↗

arXiv2019

Swirling fluid flow in flexible, expandable elastic tubes: variational approach, reductions and integrability

Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In the real-life applications like blood flow, there is often an additional complexity of vorticity being present in the fluid. We present a theory for the dynamics of interaction of fluids and structures. The equations are derived using the variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and unshearable tube with a straight centerline. In the absence of vorticity, our model reduces to previous models considered in the literature, yielding the equations of conservation of fluid momentum, wall momentum and the fluid volume. We show that even when the vorticity is present, but is kept at a constant value, the case of an inextensible, unshearable and straight tube with elastics walls carrying a fluid allows an alternative formulation, reducing to a single compact equation for the back-to-labels map instead of three conservation equations. That single equation shows interesting instability in solutions when the vorticity exceeds a certain threshold. Furthermore, the equation in stable regime can be reduced to Boussinesq-type, KdV and Monge-Ampère equations equations in several appropriate limits, namely, the first two in the limit of long time and length scales and the third one in the additional limit of the small cross-sectional area. For the unstable regime, we numerical solutions demonstrate the spontaneous appearance of large oscillations in the cross-sectional area.

physics.flu-dyn↗

arXiv2019

On the Normal Force and Static Friction Acting on a Rolling Ball Actuated by Internal Point Masses

The goal of this paper is to investigate the normal and tangential forces acting at the point of contact between a horizontal surface and a rolling ball actuated by internal point masses moving in the ball's frame of reference. The normal force and static friction are derived from the equations of motion for a rolling ball actuated by internal point masses that move inside the ball's frame of reference, and, as a special case, a rolling disk actuated by internal point masses. The masses may move along one-dimensional trajectories fixed in the ball's and disk's frame. The dynamics of a ball and disk actuated by masses moving along one-dimensional trajectories are simulated numerically and the minimum coefficients of static friction required to prevent slippage are computed.

physics.class-ph↗

arXiv2019

Integrability and Chaos in Figure Skating

We derive and analyze a three dimensional model of a figure skater. We model the skater as a three-dimensional body moving in space subject to a non-holonomic constraint enforcing movement along the skate's direction and holonomic constraints of continuous contact with ice and pitch constancy of the skate. For a static (non-articulated) skater, we show that the system is integrable if and only if the projection of the center of mass on skate's direction coincides with the contact point with ice and some mild (and realistic) assumptions on the directions of inertia's axes. The integrability is proved by showing the existence of two new constants of motion linear in momenta, providing a new and highly nontrivial example of an integrable non-holonomic mechanical system. We also consider the case when the projection of the center of mass on skate's direction does not coincide with the contact point and show that this non-integrable case exhibits apparent chaotic behavior, by studying the divergence of nearby trajectories We also demonstrate the intricate behavior during the transition from the integrable to chaotic case. Our model shows many features of real-life skating, especially figure skating, and we conjecture that real-life skaters may intuitively use the discovered mechanical properties of the system for the control of the performance on ice.

nlin.SI↗