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At least 307 records · Page 17

From Latent Dynamics to Meaningful Representations

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learnt representations meaningful. For this the typical approach is to regularize the learned representation through prior probability distributions. However such priors are usually unavailable or are ad hoc. To deal with this, recent efforts have shifted towards leveraging the insights from physical principles to guide the learning process. In this spirit, we propose a purely dynamics-constrained representation learning framework. Instead of relying on predefined probabilities, we restrict the latent representation to follow overdamped Langevin dynamics with a learnable transition density — a prior driven by statistical mechanics. We show this is a more natural constraint for representation learning in stochastic dynamical systems, with the crucial ability to uniquely identify the ground truth representation. We validate our framework for different systems including a real-world fluorescent DNA movie dataset. Here, we show that our algorithm can uniquely identify orthogonal, isometric and meaningful latent representations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hydrodynamic theory of scrambling in chaotic long-range interacting systems

The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a mean-field theory of out-of-time-ordered commutators in locally interacting quantum chaotic systems at high energy density. In systems with power-law interactions, the corresponding fractional-derivative FKPP equation provides an analogous mean-field theory. However, the fractional FKPP description is potentially subject to strong quantum fluctuation effects, so it is not clear a priori if it provides a suitable effective description for generic chaotic systems with power-law interactions. Here, in this work, we study this problem using a model of coupled quantum dots with interactions decaying as 1/r α , where each dot hosts N degrees of freedom. The large-N limit corresponds to the mean-field description, while quantum fluctuations contributing to the OTOC can be modeled by 1/N corrections consisting of a cutoff function and noise. Within this framework, we show that the parameters of the effective theory can be chosen to reproduce the butterfly light cone scalings previously found for N=1 and generic finite N. In order to reproduce these scalings, the fractional index μ in the FKPP equation needs to be shifted from the naïve value of μ=2⁢α–1 to a renormalized value μ=2⁢α–2. We provide supporting analytic evidence for the cutoff model and numerical confirmation for the full fractional FKPP equation with cutoff and noise.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Control-Affine Schrödinger Bridge and Generalized Bohm Potential

From a stochastic control perspective, the Schrödinger bridge is a density-valued continuous curve parameterized by time that connects a given pair of initial and terminal probability densities via minimum effort controlled Brownian motion. The control-affine Schrödinger bridge extends this idea to a generic control-affine Itô diffusion, possibly with an additive state cost. Here, in this letter, we recast the necessary conditions of optimality for the control-affine Schrödinger bridge problem as a two point boundary value problem for a quantum mechanical Schrödinger PDE with complex potential. This complex-valued potential is a generalization of the real-valued Bohm potential in quantum mechanics. Our derived potential is akin to the optical potential in nuclear physics where the real part of the potential encodes elastic scattering (transmission of wave function), and the imaginary part encodes inelastic scattering (absorption of wave function). The key takeaway is that the process noise that drives the evolution of probability densities induces an absorbing medium in the evolution of wave function. These results make new connections between control theory and non-equilibrium statistical mechanics through the lens of quantum mechanics.

Markov processes↗

Numerical methods for fractional Fokker–Planck equation with multiplicative Marcus Lévy noises

The Fokker–Planck equation (FPE) is an important deterministic tool for investigating stochastic dynamical systems. In this paper, we consider the space-time fractional FPE driven by multiplicative Marcus Lévy noises. Efficient numerical schemes are presented to solve the equations. Stability and convergence of the methods are also discussed. We give some numerical experiments to validate our schemes, and examine the effects of parameters on solutions. Additionally, we analyze the maximal likely trajectories and the critical time for the change of the most probability location.

Mathematics↗

NRAP-Open-IAM Multisegmented Wellbore Reduced-Order Model

Geologic carbon storage is one of the promising strategies to mitigate climate change by reducing the emission of carbon dioxide to the atmosphere. As part of the National Risk Assessment Partnership (NRAP), a systems-level stochastic analysis tool called the open source integrated assessment model, NRAP-Open-IAM, has been developed to estimate and manage the risk of containment loss at a geological carbon sequestration site. NRAP-Open-IAM contains several wellbore leakage model components that estimate the fluid leak rate that may occur through compromised legacy wells due to the increase in pressure resulting from CO 2 injection activities. Coupled to a reservoir component model, these components estimate the leakage of CO 2 and/or brine from a storage reservoir to overlying aquifer layers and the atmosphere through legacy wells. This report presents the theoretical framework and quality testing of the multisegmented wellbore reduced-order model. The model allows for segmenting of the legacy wells passing through the overlying stratigraphy into several intervals to simulate a site’s specific stratigraphic and hydrogeologic properties. For quality assurance, the analytical model is validated against numerical reservoir flow simulations for single and multiple aquifer(s) models. The results indicate that the model accurately predicts the transport of two-phase fluids (brine and injected CO 2 ) through the well over time. A detailed description of the model helps users to understand the model and provides a basis for future improvements.

58 GEOSCIENCES↗

Electron Cooling for the Antiproton Accumulator

A possibility to utilize electron cooling in the Fermilab Antiproton Accumulator (AA) is studied. It is shown that, for the existing stochastic cooling system and 0.5 Ampere x 10 m of electron cooler, the accumulated antiproton current could be increased up to 0.5-1.0 Ampere with required or lower longitudinal and transverse emittances.

43 PARTICLE ACCELERATORS↗

The mapping & avoidance of high order cavity modes

In this paper a technique developed in 2016 is presented for mapping the multidimensional, multi-mode high order mode landscape of a beam driven super conducting RF cavity. The initial use case for this technique was intended to allow longitudinal gradient control of a beam driven super conducting cavity while simultaneously avoiding many dangerous high order modes and excessive component stresses. This paper will focus on the stability and component stress considerations of the 56MHz superconducting cavity, located in the 4 o’clock sector interaction region of the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory. The 56MHz cavity is intended to work in conjunction with the Stochastic Cooling system to improve the longitudinal confinement in the central 197MHz RF bucket and thus increase the integrated luminosity during heavy ion beam runs at RHIC.

43 PARTICLE ACCELERATORS↗

Maximizing RHIC Deliverable Luminosity with Dynamic Telescopic Beta* Squeeze

To benefit fully from the exceptional performance of the Relativistic Heavy Ions Collider (RHIC) Stochastic Cooling system during heavy ions physics store, the betatron amplitude β ∗ at a given col lision point (IP) can be squeezed from its design value by using the available space in the quadrupole triplets from smaller beam emittances. This should allow reaching new heights in deliverable lumi nosity for both STAR and PHENIX experiments. Prior to 2014, RHIC lattice designs only squeezed the interaction regions (IR’s) down to β ∗ = 0.70 m. To get past this limitation, one can use a telescopic scheme where the non-experimental insertions surrounding STAR and PHENIX are used to generate and close a β-beat wave contributing to the final squeeze in the two IP’s of interest. The following presents the various steps of the implementation in RHIC of this telescopic scheme and the corresponding changes in collision rates and specific luminosity. A full feasibility study with a review of hardware and beam dynamics limitations is also included.

43 PARTICLE ACCELERATORS↗

Aircraft adaptive learning control

The optimal control theory of stochastic linear systems is discussed in terms of the advantages of distributed-control systems, and the control of randomly-sampled systems. An optimal solution to longitudinal control is derived and applied to the F-8 DFBW aircraft. A randomly-sampled linear process model with additive process and noise is developed.

Lee, P. S. T.↗

Minimum information modelling of structural systems with uncertain parameters

Work is reviewed wherein the design of active structural control is formulated as the mean-square optimal control of a linear mechanical system with stochastic parameters. In practice, a complete probabilistic description of model parameters can never be provided by empirical determinations, and a suitable design approach must accept very limited a priori data on parameter statistics. In consequence, the mean-square optimization problem is formulated using a complete probability assignment which is made to be consistent with available data but maximally unconstrained otherwise through use of a maximum entropy principle. The ramifications of this approach for both robustness and large dimensionality are illustrated by consideration of the full-state feedback regulation problem.

Hyland, D. C.↗

Optimal interpolation and the Kalman filter

The estimation theory of stochastic-dynamic systems is described and used in a numerical study of optimal interpolation. The general form of data assimilation methods is reviewed. The Kalman-Bucy, KB filter, and optimal interpolation (OI) filters are examined for effectiveness in performance as gain matrices using a one-dimensional form of the shallow-water equations. Control runs in the numerical analyses were performed for a ten-day forecast in concert with the OI method. The effects of optimality, initialization, and assimilation were studied. It was found that correct initialization is necessary in order to localize errors, especially near boundary points. Also, the use of small forecast error growth rates over data-sparse areas was determined to offset inaccurate modeling of correlation functions near boundaries.

Cohn, S.↗

Filtered Mass Density Function for Design Simulation of High Speed Airbreathing Propulsion Systems

The objective of this research is to develop and implement new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. We have just completed two (2) years of Phase I of this research. This annual report provides a brief and up-to-date summary of our activities during the period: September 1, 2000 through August 31, 2001. In the work within the past year, a methodology termed "velocity-scalar filtered density function" (VSFDF) is developed and implemented for large eddy simulation (LES) of turbulent flows. In this methodology the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function (PDF) of all of the components of the velocity and scalar vectors. An exact transport equation is derived for the VSFDF in which the effects of the unresolved SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source terms appear in closed form. The remaining unclosed terms in this equation are modeled. A system of stochastic differential equations (SDEs) which yields statistically equivalent results to the modeled VSFDF transport equation is constructed. These SDEs are solved numerically by a Lagrangian Monte Carlo procedure. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed by comparison with results obtained by an Eulerian LES procedure in which the corresponding transport equations for the first two SGS moments are solved. The unclosed SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source in the Eulerian LES are replaced by corresponding terms from VSFDF equation. The consistency of the results is then analyzed for a case of two dimensional mixing layer.

Drozda, T. G.↗