arXiv subjects

Michael Chertkov

Publications and source records attributed to Michael Chertkov.

At least 19 recordsLinked to original sources

arXiv2026

Driven Quantum Stars as Controlled Primitives for Real-Time Spin Dynamics

Quantum advantage in real-time spin dynamics should be assessed against the strongest relevant classical substitutes, not merely against the qubit nature of the microscopic system. We develop a physics-based diagnostic for this boundary by reducing a qubit spin model to a spin-Landau--Lifshitz (LL) classical sector and organizing the residual quantum sector as controlled corrections. The control parameter is graph coordination: we study a spin star with $d$ leaves and $O(1/d)$ hub--leaf couplings. In its homogeneous form the star benchmarks the transition from LL-substitutable dynamics to genuinely quantum, discrete-sector interference; in its fully driven form, with time-dependent fields and bilinear couplings, it is the basic message-passing primitive for tree and loopy spin structures. For coherent-state return amplitudes we prove exact leaf elimination and derive a continuous-time $1/d$ hierarchy. L0 is a driven one-spin weak-mean-field theory, while G1 is a Gaussian nonlocal-in-time influence correction coupling leaf two-time kernels to the hub weak two-point function. On bounded finite-time windows away from zeros of the boundary amplitudes, the hierarchy gives $\log\mathcal A-\log\mathcal A_{\rm L0}=O(1/d)$ and $\log\mathcal A-\log\mathcal A_{\rm L0}-\Delta_{\rm G1}=O(1/d^2)$; numerical tests on fully driven anisotropic ensembles give slopes $-1.05$ and $-2.03$. Static, inhomogeneous, aligned, and fully driven stars provide validation rungs, and comparison with a temporal matrix-product influence-matrix baseline delineates complementary regimes. Unlike rank compression on a Trotter grid, the hierarchy is ordered by a physical parameter, formulated in continuous time, and each truncation level is itself a physical theory, with the LL sector as the high-coordination limit.

quant-ph↗

arXiv2026

Lagrangian Ellipsoid Diagnostics in Rough Two-Dimensional Synthetic Flows: Aspect-Ratio Saturation and Reduced Modeling

We develop and test a Lagrangian methodology for extracting finite-cloud geometry and reduced dynamics from particle trajectories. A cloud in a rough, incompressible, two-dimensional synthetic flow is represented by a mass/gyration ellipse describing the particle-weighted bulk and a minimum-area enclosing ellipse describing the outer envelope and its supporting particles. The homogeneous Gaussian--H"older velocity has finite Ornstein--Uhlenbeck memory, and the moving centroid is followed explicitly. The principal finding is unexpected: despite continual deformation by a non-smooth velocity field, the normalized aspect ratios of both ellipses reach broad, order-one distributions that are approximately stationary when conditioned on cloud scale. The mass ellipse is more elongated, whereas the enclosing ellipse spans a larger radial envelope and has the more scale-stable conditional shape distribution. To understand this saturation, we compare two finite-cloud descriptions of the velocity gradient. A gradient averaged over the enclosing ellipse predicts more aligned stretching than the particles experience. The resulting gradient correction supplies most of the negative contribution offsetting aligned stretching, while a smaller correction is specific to representing the evolving outer cloud by an enclosing ellipse. Finally, we demonstrate a data-to-model workflow. The measured time series is transformed to intrinsic variables, a constrained hierarchy of finite-lag stochastic models is fitted, and the models are compared on held-out realizations. The fitted coefficients and equations are specific to this synthetic experiment. The transferable contribution is the methodology: paired cloud geometries, finite-cloud coarse graining, intrinsic variables, transparent correction decomposition, and held-out validation for future simulations and experiments.

physics.flu-dyn↗

arXiv2026

Lagrangian single-particle, multi-particle and topological analyses in turbulent Rayleigh-B\'enard convection

We present three-dimensional direct numerical simulations of turbulent Rayleigh-B\'enard convection (RBC) in the Lagrangian frame of reference for Rayleigh numbers $10^5 \leq Ra \leq 10^{10}$ and a Prandtl number $Pr=0.7$ in a plane layer at an aspect ratio $L:L:H=4:4:1$ with a horizontal length $L$ and height $H$. We use particle accelerations, Lagrangian heat transfer, $Q$-$R$ invariant topology, Lagrangian particle pair dispersion, scale-dependent Lagrangian eddy viscosity, and principal component analysis (PCA) of dense particle clouds to characterise convective transport along material trajectories. By computing particle accelerations at the integration time step and controlling spectral element method signatures, we obtain robust acceleration statistics and recover Heisenberg-Yaglom behaviour. Lagrangian heat transfer is extremely intermittent: individual massless Lagrangian particles can carry convective heat fluxes up to $500$ times the global Eulerian mean, although higher-order heat flux moments decrease toward Gaussian values with increasing $Ra$. The analysis of velocity gradient invariants in the $Q$-$R$ plane along trajectories identifies a distinct topological footprint of dust-devil-like convective vortices in the quadrant of $Q>0$, $R<0$, associated with vortex stretching, plume detachment, and intense localised heat transfer. Global unconditioned pair dispersion exhibits neither extended Richardson nor Bolgiano-Obukhov scaling plateaus. Rather, scale-dependent eddy viscosity and conditioned PCA of dense particle clouds reveal that buoyancy- and shear-driven dispersion are temporally organised: rapid plume-driven ejection produces a short $t^5$-like episode, followed by sustained Richardson-like $t^3$-scaling. Thus, Lagrangian topology and cloud geometry provide mechanism-resolving diagnostics for active-scalar turbulence beyond RBC-specific global scaling laws.

physics.flu-dyn↗

arXiv2026

Analytic Bridge Diffusions for Controlled Path Generation

Most modern bridge-diffusion methods achieve finite-time transport by specifying an interpolation, Schrodinger-bridge, or stochastic-control objective and then learning the associated score or drift field with a neural network. In contrast, we identify a restricted but sufficiently broad analytically solvable class in which, for a deterministic source and a Gaussian-mixture target, the score and all intermediate marginals are explicit and protocol objectives of the type used in this paper can be differentiated without inner stochastic simulation loops. We recast the classical linear--quadratic--Gaussian stochastic-control structure as a transport problem of the Path Integral Diffusion type. Linear dynamics, Gaussian noise, and quadratic running costs reduce the bridge calculation to a matrix Riccati cascade, while the terminal state cost is replaced by a prescribed Gaussian-Mixture terminal probability density. Linear Quadratic -- Gaussian Mixture -- Path Integral Diffusion (LQ-GM-PID) thereby turns bridge diffusion from terminal target matching alone into an analytically controlled laboratory for path shaping. We demonstrate this on a 2D corridor task, a 2D multi-entrance task, and a high-dimensional study reaching d=32 and M=16 terminal modes in separate scaling sweeps. We position LQ-GM-PID as an analytically solvable reference model in which score approximations, path-shaping objectives, and protocol-learning procedures can be tested against explicit quantities.

cs.LG↗

arXiv2026

Temporal Memory for Resource-Constrained Agents: Continual Learning via Stochastic Compress-Add-Smooth

An agent that operates sequentially must incorporate new experience without forgetting old experience, under a fixed memory budget. We propose a framework in which memory is not a parameter vector but a stochastic process: a Bridge Diffusion on a replay interval $[0,1]$, whose terminal marginal encodes the present and whose intermediate marginals encode the past. New experience is incorporated via a three-step \emph{Compress--Add--Smooth} (CAS) recursion. We test the framework on the class of models with marginal probability densities modeled via Gaussian mixtures of fixed number of components~$K$ in $d$ dimensions; temporal complexity is controlled by a fixed number~$L$ of piecewise-linear protocol segments whose nodes store Gaussian-mixture states. The entire recursion costs $O(LKd^2)$ flops per day -- no backpropagation, no stored data, no neural networks -- making it viable for controller-light hardware. Forgetting in this framework arises not from parameter interference but from lossy temporal compression: the re-approximation of a finer protocol by a coarser one under a fixed segment budget. We find that the retention half-life scales linearly as $a_{1/2}\approx c\,L$ with a constant $c>1$ that depends on the dynamics but not on the mixture complexity~$K$, the dimension~$d$, or the geometry of the target family. The constant~$c$ admits an information-theoretic interpretation analogous to the Shannon channel capacity. The stochastic process underlying the bridge provides temporally coherent ``movie'' replay -- compressed narratives of the agent's history, demonstrated visually on an MNIST latent-space illustration. The framework provides a fully analytical ``Ising model'' of continual learning in which the mechanism, rate, and form of forgetting can be studied with mathematical precision.

cs.LG↗

arXiv2026

Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents

Independent sample generation is the prevailing paradigm in modern diffusion-based generative models of AI. We ask a different question: can samples \emph{coordinate} through shared population statistics to transport probability mass more efficiently? We introduce Mean-Field Path-Integral Diffusion (MF-PID), a framework in which samples are promoted to interacting agents whose drift depends self-consistently on the evolving population density. The coupling converts distribution matching into a McKean--Vlasov extension of the stochastic optimal transport problem, unifying generative modeling and multi-agent control under the same Hamilton--Jacobi--Bellman/Kolmogorov--Fokker--Planck duality. We identify two analytically tractable regimes: a Linear--Quadratic--Gaussian (LQG) benchmark in which the infinite-dimensional mean-field system reduces to a finite set of Riccati and linear ODEs, and a Gaussian-mixture regime governed by a piecewise-constant protocol that preserves closed-form solvability. For a quadratic interaction potential with schedule $\beta_t$ and zero base drift we prove that the self-consistent MF guidance is the \emph{exact} linear interpolant between initial and target global means -- a result that holds for arbitrary initial and target densities and any $\beta_t$. Applied to demand-response control of energy systems, where agents aggregated into an ensemble are energy consumers (e.g.\ thermal zones within a building), MF-PID achieves 19--24\% reductions in cumulative control energy over independent-agent baselines while matching the prescribed terminal distribution exactly, and reveals how coordination redistributes actuation effort across heterogeneous sub-populations.

math.OC↗

arXiv2025

Adaptive Path Integral Diffusion: AdaPID

Diffusion-based samplers -- Score Based Diffusions, Bridge Diffusions and Path Integral Diffusions -- match a target at terminal time, but the real leverage comes from choosing the schedule that governs the intermediate-time dynamics. We develop a path-wise schedule -- selection gramework for Harmonic PID with a time-varying stiffness, exploiting Piece-Wise-Constant(PWC) parametrizations and a simple hierarchical refinement. We introduce schedule-sensitive Quality-of-Sampling (QoS) diagnostics. Assuming a Gaussian-Mixture (GM) target, we retain closed-form Green functions' ration and numerically stable, Neural-Network free oracles for predicted-state maps and score. Experiments in 2D show that QoS driven PWC schedules consistently improve early-exit fidelity, tail accuracy, conditioning of the dynamics, and speciation (label-selection) timing at fixed integration budgets.

cs.LG↗

arXiv2025

Generative Stochastic Optimal Transport: Guided Harmonic Path-Integral Diffusion

We introduce Guided Harmonic Path-Integral Diffusion (GH-PID), a linearly-solvable framework for guided Stochastic Optimal Transport (SOT) with a hard terminal distribution and soft, application-driven path costs. A low-dimensional guidance protocol shapes the trajectory ensemble while preserving analytic structure: the forward and backward Kolmogorov equations remain linear, the optimal score admits an explicit Green-function ratio, and Gaussian-Mixture Model (GMM) terminal laws yield closed-form expressions. This enables stable sampling and differentiable protocol learning under exact terminal matching. We develop guidance-centric diagnostics -- path cost, centerline adherence, variance flow, and drift effort -- that make GH-PID an interpretable variational ansatz for empirical SOT. Three navigation scenarios illustrated in 2D: (i) Case A: hand-crafted protocols revealing how geometry and stiffness shape lag, curvature effects, and mode evolution; (ii) Case B: single-task protocol learning, where a PWC centerline is optimized to minimize integrated cost; (iii) Case C: multi-expert fusion, in which a commander reconciles competing expert/teacher trajectories and terminal beliefs through an exact product-of-experts law and learns a consensus protocol. Across all settings, GH-PID generates geometry-aware, trust-aware trajectories that satisfy the prescribed terminal distribution while systematically reducing integrated cost.

cs.LG↗

arXiv2025

Sampling Decisions: Exact Path-Space Control for Physics-Informed Generative Sampling

Scientific generative models must turn tractable local decisions into globally correlated samples that respect physical constraints. We introduce Sampling Decisions, a finite-horizon framework in which a structured object is assembled on a growing state graph and corrected globally by an exact path-space control law. For a prescribed Gibbs target, the corrected law is the unique relative-entropy projection of a sequential prior and is realized by a Doob h-transform with a linear backward desirability recursion. The same object admits equivalent interpretations as a KL-optimal controller, a one-sided Schrodinger transport, and an ideal value or flow function for autoregressive and GFlowNet-type generation. A route-resolved formulation yields a finite-particle algorithm, whose transition kernels and terminal law converge as the path budget grows. For binary graphical models, we prove a structural cancellation theorem: every fixed singleton-product prior disappears from the population correction, so improved one-point marginals do not alter the exact generative dynamics. The relevant information is conditional and prefix dependent. Statistical physics supplies this structure through a Local-Boltzmann prior that absorbs interactions as spins are revealed, while optimal path-space control supplies the missing look-ahead field from the unrevealed subgraph. On exactly enumerable Ising grids, this physics-informed proposal increases effective sample size by factors of about ten to nearly one thousand relative to product proposals and reaches the exact-target reference band at the tested budgets. On a larger 10*10 grid, beyond exact enumeration, the same hierarchy persists: Local-Boltzmann guidance avoids the severe weight collapse of product proposals and approaches a long-run MCMC baseline on the reported diagnostics.

cs.LG↗

arXiv2025

Lagrangian Attention Tensor Networks for Velocity Gradient Statistical Modeling

Direct numerical simulation of turbulence at realistic Reynolds numbers is still beyond current computational capability, necessitating models that reduce the number of resolved spatial scales. Motivated by phenomenology and recent data-driven works based on universality of the smallest scales in fully developed turbulence, the statistical dynamics of the velocity gradient tensor (VGT) at the Kolmogorov scale become of critical importance in advancing turbulence models. Physics-informed machine learning has found considerable success in exploiting large datasets taken from direct numerical simulation of Navier-Stokes to improve models for the evolution of the VGT. In this work, we follow the long line of blending physical insight with data analysis to simultaneously advance both the modeling and understanding of the phenomenology of the VGT. Using the intimate connection between VGT evolution and fluid deformation, we develop the Lagrangian attention tensor network approach that significantly improves over current physics-informed machine learning methods. We demonstrate state-of-the-art performance in both a-priori and a-posteriori metrics, before interpreting the trained attention mechanisms to discover a surprising connection between the history of the strain-rate-tensor and the pressure Hessian.

physics.flu-dyn↗

arXiv2024

Harmonic Path Integral Diffusion

In this manuscript, we present a novel approach for sampling from a continuous multivariate probability distribution, which may either be explicitly known (up to a normalization factor) or represented via empirical samples. Our method constructs a time-dependent bridge from a delta function centered at the origin of the state space at $t=0$, optimally transforming it into the target distribution at $t=1$. We formulate this as a Stochastic Optimal Control problem of the Path Integral Control type, with a cost function comprising (in its basic form) a quadratic control term, a quadratic state term, and a terminal constraint. This framework, which we refer to as Harmonic Path Integral Diffusion (H-PID), leverages an analytical solution through a mapping to an auxiliary quantum harmonic oscillator in imaginary time. The H-PID framework results in a set of efficient sampling algorithms, without the incorporation of Neural Networks. The algorithms are validated on two standard use cases: a mixture of Gaussians over a grid and images from CIFAR-10. The transparency of the method allows us to analyze the algorithms in detail, particularly revealing that the current weighted state is an order parameter for the dynamic phase transition, signaling earlier, at $t<1$, that the sample generation process is almost complete. We contrast these algorithms with other sampling methods, particularly simulated annealing and path integral sampling, highlighting their advantages in terms of analytical control, accuracy, and computational efficiency on benchmark problems. Additionally, we extend the methodology to more general cases where the underlying stochastic differential equation includes an external deterministic, possibly non-conservative force, and where the cost function incorporates a gauge potential term.

stat.ML↗

arXiv2024

Physics-Informed Building Occupancy Detection: a Switching Process with Markov Regime

Energy efficiency of buildings is considered to be one of the major means of achieving the net-zero carbon goal around the world. The big part of the energy savings are supposed to be coming from optimizing the operation of the building heating, ventilation, and air conditioning (HVAC) systems. There is a natural trade-off between the energy efficiency and the indoor comfort level, and finding an optimal operating schedule/regime requires knowing the occupancy of different spaces inside of the building. Moreover, the COVID-19 pandemic has also revealed the need to sustain the high quality of the indoor air in order to reduce the risk of spread of infection. Occupancy detection from indoor sensors is thus an important practical problem. In the present paper, we propose detection of occupancy based on the carbon dioxide measurements inside the building. In particular, a new approach based on the, so-called, switching auto-regressive process with Markov regime is presented and justified by the physical model of the carbon dioxide concentration dynamics. We demonstrate the efficiency of the method compared to simple Hidden Markov approaches on simulated and real-life data. We also show that the model is flexible and can be generalized to account for different ventilation regimes, simultaneously detecting the occupancy and the ventilation rate.

eess.SY↗

arXiv2024

Physics-Guided Actor-Critic Reinforcement Learning for Swimming in Turbulence

Turbulent diffusion causes particles placed in proximity to separate. We investigate the required swimming efforts to maintain an active particle close to its passively advected counterpart. We explore optimally balancing these efforts by developing a novel physics-informed reinforcement learning strategy and comparing it with prescribed control and physics-agnostic reinforcement learning strategies. Our scheme, coined the actor-physicist, is an adaptation of the actor-critic algorithm in which the neural network parameterized critic is replaced with an analytically derived physical heuristic function, the physicist. We validate the proposed physics-informed reinforcement learning approach through extensive numerical experiments in both synthetic BK and more realistic Arnold-Beltrami-Childress flow environments, demonstrating its superiority in controlling particle dynamics when compared to standard reinforcement learning methods.

eess.SY↗

arXiv2024

Mixing Artificial and Natural Intelligence: From Statistical Mechanics to AI and Back to Turbulence

The paper reflects on the future role of AI in scientific research, with a special focus on turbulence studies, and examines the evolution of AI, particularly through Diffusion Models rooted in non-equilibrium statistical mechanics. It underscores the significant impact of AI on advancing reduced, Lagrangian models of turbulence through innovative use of deep neural networks. Additionally, the paper reviews various other AI applications in turbulence research and outlines potential challenges and opportunities in the concurrent advancement of AI and statistical hydrodynamics. This discussion sets the stage for a future where AI and turbulence research are intricately intertwined, leading to more profound insights and advancements in both fields.

cs.LG↗

arXiv2024

Space-Time Diffusion Bridge

In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground Truth (GT) samples. Central to our method is the integration of space-time mixing strategies that extend across temporal and spatial dimensions. Our methodology is underpinned by three interrelated stochastic processes designed to enable optimal transport from an easily tractable initial probability distribution to the target distribution represented by the GT samples: (a) linear processes incorporating space-time mixing that yield Gaussian conditional probability densities, (b) their diffusion bridge analogs that are conditioned to the initial and final state vectors, and (c) nonlinear stochastic processes refined through score-matching techniques. The crux of our training regime involves fine-tuning the nonlinear model, and potentially the linear models -- to align closely with the GT data. We validate the efficacy of our space-time diffusion approach with numerical experiments, laying the groundwork for more extensive future theory and experiments to fully authenticate the method, particularly providing a more efficient (possibly simulation-free) inference.

stat.ML↗

arXiv2023

Deciphering the Dance of the Winds and Waves: Unraveling Anomalous Dynamics in Floating Offshore Wind Turbines

We study the Floating Offshore Wind Turbine (FOWT) dynamic response to high wind velocity scenarios utilizing an extensive Markov Chain Monte Carlo simulation involving 10,000 trials of a reduced model from \cite{betti_development_2014} with a blade-pitch PID controller. The research emphasizes analysis of extreme events in surge, pitch and heave of FOWT, identifying and categorizing them based on their statistics, correlations and causal relations to wind and waves. A significant discovery is the differentiation of anomalies into short-correlated and long-correlated types, with the latter primarily influenced by wind conditions. For example, one of our findings is that while specific wave conditions may amplify anomalies, wind remains the predominant factor in long-term anomalous pitch behaviors. We anticipate that further development of this analysis of the operation's critical extreme events will be pivotal for advancing control strategies and design considerations in FOWTs, accommodating the turbulent environment they encounter.

math.DS↗

arXiv2023

System-Wide Emergency Policy for Transitioning from Main to Secondary Fuel

Faced with the complexities of managing natural gas-dependent power system amid the surge of renewable integration and load unpredictability, this study explores strategies for navigating emergency transitions to costlier secondary fuels. Our aim is to develop decision-support tools for operators during such exigencies. We approach the problem through a Markov Decision Process (MDP) framework, accounting for multiple uncertainties. These include the potential for dual-fuel generator failures and operator response during high-pressure situations. Additionally, we consider the finite reserves of primary fuel, governed by gas-flow partial differential equations (PDEs) and constrained by nodal pressure. Other factors include the variability in power forecasts due to renewable generation and the economic impact of compulsory load shedding. For tractability, we address the MDP in a simplified context, replacing it by Markov Processes evaluated against a selection of policies and scenarios for comparison. Our study considers two models for the natural gas system: an over-simplified model tracking linepack and a more nuanced model that accounts for gas flow network heterogeneity. The efficacy of our methods is demonstrated using a realistic model replicating Israel's power-gas infrastructure.

eess.SY↗

arXiv2023

Physics informed machine learning with Smoothed Particle Hydrodynamics: Hierarchy of reduced Lagrangian models of turbulence

Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and investigates the effects of enforcing physical structure through Smoothed Particle Hydrodynamics (SPH) versus relying on neural networks (NN)s as universal function approximators. Starting from Neural Network (NN) parameterizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed in order to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using Automatic Differentiation (AD) and Sensitivity Analysis (SA). Each model within the hierarchy is trained on two data sets associated with weekly compressible Homogeneous Isotropic Turbulence (HIT): (1) a validation set using weakly compressible SPH; and (2) a high fidelity set from Direct Numerical Simulations (DNS). Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales.

physics.flu-dyn↗