A Kushner–Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification

Sarkar, S.; Chowdhury, Shubhankar Roy; Venugopal, Mamatha; Vasu, Ram Mohan; Roy, Debasish

doi:10.1016/j.physd.2013.12.007

Cited by 15 publications

(13 citation statements)

References 35 publications

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“…However an exact solution of the KS equation is available only under the restriction of a linear measurement operator and the assumption that the noises involved are Gaussian. An attempt has been made to solve a discretized version of the KS equation in a Monte Carlo setting [26] that provides an additive correction to each predicted realization of the parameter process. The additive gain-like term is arrived at using tools from stochastic calculus and the detailed derivation of the same is provided in [22].…”

Section: Evolutionary Stochastic Reconstruction Methodsmentioning

confidence: 99%

Diffraction tomography from intensity measurements: an evolutionary stochastic search to invert experimental data

et al. 2014

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We develop iterative diffraction tomography algorithms, which are similar to the distorted Born algorithms, for inverting scattered intensity data. Within the Born approximation, the unknown scattered field is expressed as a multiplicative perturbation to the incident field. With this, the forward equation becomes stable, which helps us compute nearly oscillation-free solutions that have immediate bearing on the accuracy of the Jacobian computed for use in a deterministic Gauss-Newton (GN) reconstruction. However, since the data are inherently noisy and the sensitivity of measurement to refractive index away from the detectors is poor, we report a derivative-free evolutionary stochastic scheme, providing strictly additive updates in order to bridge the measurement-prediction misfit, to arrive at the refractive index distribution from intensity transport data. The superiority of the stochastic algorithm over the GN scheme for similar settings is demonstrated by the reconstruction of the refractive index profile from simulated and experimentally acquired intensity data.

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Section: Evolutionary Stochastic Reconstruction Methodsmentioning

confidence: 99%

Diffraction tomography from intensity measurements: an evolutionary stochastic search to invert experimental data

et al. 2014

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“…Even with scrambling and blending, a search scheme that always chooses to update the particles would The dimensionality curse, which besets many stochastic search schemes including most stochastic filters with the necessity of an exponentially exploding ensemble size, comes in the way of solving inverse problems with a large number of unknowns. To a large extent, the particle degeneracy problems encountered by weight-based schemes are circumvented in the additive-update strategies that attempt at 'healing' the bad particles instead of eliminating them altogether [7]. However, even with such an approach, the quality of solutions is highly dependent on the ensemble size, e n , as has been proved in [24].…”

Section: Relaxation and Selectionmentioning

confidence: 99%

A stochastically evolving non-local search and solutions to inverse problems with sparse data

Venugopal

Vasu

Roy

2016

Probabilistic Engineering Mechanics

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Building upon our earlier work of a martingale approach to global optimization, a powerful stochastic search scheme for the global optimum of cost functions is proposed on the basis of change of measures on the states that evolve as diffusion processes and splitting of the statespace along the lines of a Bayesian game. To begin with, the efficacy of the optimizer, when contrasted with one of the most efficient existing schemes, is assessed against a family of N phard benchmark problems. Then, using both simulated-and experimental data, potentialities of the new proposal are further explored in the context of an inverse problem of significance in medical imaging, wherein the superior reconstruction features of a global search vis-à-vis the commonly adopted local or quasi-local schemes are brought into relief.

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“…Neglecting contributions from tr ∇uR T ∇uR T and tr(RR) T , the discrete Hamiltonian finally takes the following form. The governing dynamics for the system and bath variables, described through Hamilton's equations in terms of the displacement DOFs and the momenta, are given by the equation pairs (11,12) and (13,14) …”

Section: Formulation Of Discrete Hamiltonianmentioning

confidence: 99%

“…In Fig.2, we also see that simulation using the standard GLE fails to produce the steady-state fluctuations. The proposed GLE is further tested in the context of an inverse problem, wherein using it as a process model, a stochastic projection on the experimental MSD data through a nonlinear filter [13] leads to an estimate quite close to the measurement (Fig.3). However, the same exercise with the standard GLE as process model (for the same Monte Carlo sample size) produces a completely different response estimate.…”

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confidence: 99%

Internal noise-driven generalized Langevin equation from a nonlocal continuum model

et al. 2015

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Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree-of-freedom (DOF), is derived. The GLE features a memory dependent multiplicative or internal noise, which appears upon recognising that the micro-rotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the new GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum. A constraint equation, similar to a fluctuation dissipation theorem (FDT), is shown to statistically relate the internal noise to the other parameters in the GLE.PACS numbers: 46.05.+b, 05.40.Ca, 78.35.+c As the space/time length scale in the forcing or the triggered deformation mechanism becomes comparable with the internal length scale of the material, the system response at the macro-continuum scale is significantly influenced by the material microstructure. This renders the classical continuum hypothesis of strictly local interactions, or its possible extension using adiabatic continuation arguments, untenable in the modeling of such response. Non-local modeling techniques such as micropolar [1], micromorphic [1] or gradient [2] theories, which aim at incorporating long-range inter-particle interactions, bring forth microstructural effects by introducing material length scales in the constitutive formulation. In materials like polymers, granular solids etc. where the length scale is of the macroscopic order, long-range effects could predominate and, in such cases, predictions through nonlocal models, unlike the the classical continuum model, are in closer conformity with experimental observations. If a continuum model can be replaced by a collection of harmonic oscillators and the focus is on the motion of a small region represented by a particle (an oscillator) with a single predominant translational degree-of-freedom (DOF), one arrives at a generalized Langevin equation (GLE) for the DOF after including the coupling effects from the neighboring oscillators [3]. The GLE, an expedient modeling tool that replaces the infinite dimensional continuum, is widely used in areas such as soft condensed matter physics and cell biology. Despite the correspondence as above between the GLE and the continuum, standard forms of the GLE do not include length scale information characteristic of nonlocal continuum theories and are therefore not equipped to describe the physically relevant microstructural effects.This work is partly motivated by the experimental data shown in Fig.1 (adapted from Fig. 6 of [4]). These correspond to the mean square displacement (MSD) plots of temperature-induced Brownian particles in a polyvinyl alcohol (PVA) slab, extracte...

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A Kushner–Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification

Cited by 15 publications

References 35 publications

Diffraction tomography from intensity measurements: an evolutionary stochastic search to invert experimental data

Diffraction tomography from intensity measurements: an evolutionary stochastic search to invert experimental data

A stochastically evolving non-local search and solutions to inverse problems with sparse data

Internal noise-driven generalized Langevin equation from a nonlocal continuum model

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