State and parameter estimation using Monte Carlo evaluation of path integrals

Transferring information from observations of a dynamical system to estimate the fixed parameters and unobserved states of a system model can be formulated as the evaluation of a discrete time path integral in model state space. The observations serve as a guiding potential working with the dynamical rules of the model to direct system orbits in state space. The path integral representation permits direct numerical evaluation of the conditional mean path through the state space as well as conditional moments about this mean. Using a Monte Carlo method for selecting paths through state space we show how these moments can be evaluated and demonstrate in an interesting model system the explicit influence of the role of transfer of information from the observations. We address the question of how many observations are required to estimate the unobserved state variables, and we examine the assumptions of Gaussianity of the underlying conditional probability.Comment: Submitted to the Quarterly Journal of the Royal Meteorological Society, 19 pages, 5 figure

Automatic Construction of Predictive Neuron Models through Large Scale Assimilation of Electrophysiological Data.

We report on the construction of neuron models by assimilating electrophysiological data with large-scale constrained nonlinear optimization. The method implements interior point line parameter search to determine parameters from the responses to intracellular current injections of zebra finch HVC neurons. We incorporated these parameters into a nine ionic channel conductance model to obtain completed models which we then use to predict the state of the neuron under arbitrary current stimulation. Each model was validated by successfully predicting the dynamics of the membrane potential induced by 20-50 different current protocols. The dispersion of parameters extracted from different assimilation windows was studied. Differences in constraints from current protocols, stochastic variability in neuron output, and noise behave as a residual temperature which broadens the global minimum of the objective function to an ellipsoid domain whose principal axes follow an exponentially decaying distribution. The maximum likelihood expectation of extracted parameters was found to provide an excellent approximation of the global minimum and yields highly consistent kinetics for both neurons studied. Large scale assimilation absorbs the intrinsic variability of electrophysiological data over wide assimilation windows. It builds models in an automatic manner treating all data as equal quantities and requiring minimal additional insight

Basin structure of optimization based state and parameter estimation

Most data based state and parameter estimation methods require suitable initial values or guesses to achieve convergence to the desired solution, which typically is a global minimum of some cost function. Unfortunately, however, other stable solutions (e.g., local minima) may exist and provide suboptimal or even wrong estimates. Here we demonstrate for a 9-dimensional Lorenz-96 model how to characterize the basin size of the global minimum when applying some particular optimization based estimation algorithm. We compare three different strategies for generating suitable initial guesses and we investigate the dependence of the solution on the given trajectory segment (underlying the measured time series). To address the question of how many state variables have to be measured for optimal performance, different types of multivariate time series are considered consisting of 1, 2, or 3 variables. Based on these time series the local observability of state variables and parameters of the Lorenz-96 model is investigated and confirmed using delay coordinates. This result is in good agreement with the observation that correct state and parameter estimation results are obtained if the optimization algorithm is initialized with initial guesses close to the true solution. In contrast, initialization with other exact solutions of the model equations (different from the true solution used to generate the time series) typically fails, i.e. the optimization procedure ends up in local minima different from the true solution. Initialization using random values in a box around the attractor exhibits success rates depending on the number of observables and the available time series (trajectory segment).Comment: 15 pages, 2 figure

Synchronicity From Synchronized Chaos

The synchronization of loosely coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical notion of synchronicity. Effectively unpredictable chaotic systems, coupled through only a few variables, commonly exhibit a predictable relationship that can be highly intermittent. We argue that the phenomenon closely resembles the notion of meaningful synchronicity put forward by Jung and Pauli if one identifies "meaningfulness" with internal synchronization, since the latter seems necessary for synchronizability with an external system. Jungian synchronization of mind and matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system as in meteorological data assimilation. Internal synchronization provides a recipe for combining different models of the same objective process, a configuration that may also describe the functioning of conscious brains. In contrast to Pauli's view, recent developments suggest a materialist picture of semi-autonomous mind, existing alongside the observed world, with both exhibiting a synchronistic order. Basic physical synchronicity is manifest in the non-local quantum connections implied by Bell's theorem. The quantum world resides on a generalized synchronization "manifold", a view that provides a bridge between nonlocal realist interpretations and local realist interpretations that constrain observer choice .Comment: 1) clarification regarding the connection with philosophical synchronicity in Section 2 and in the concluding section 2) reference to Maldacena-Susskind "ER=EPR" relation in discussion of role of wormholes in entanglement and nonlocality 3) length reduction and stylistic changes throughou

Reduction of a Vehicle Multibody Dynamic Model Using Homotopy Optimization

The original publication is available at: Hall, A., Uchida, T., Loh, F., Schmitke, C., & Mcphee, J. (2013). Reduction of a Vehicle Multibody Dynamic Model Using Homotopy Optimization. Archive of Mechanical Engineering, LX(1). https://doi.org/10.2478/meceng-2013-0002Despite the ever-increasing computational power of modern processors, the reduction of complex multibody dynamic models remains an important topic of investigation, particularly for design optimization, sensitivity analysis, parameter identification, and controller tuning tasks, which can require hundreds or thousands of simulations. In this work, we first develop a high-fidelity model of a production sports utility vehicle in Adams/Car. Single-link equivalent kinematic quarter-car (SLEKQ, pronounced “sleek”) models for the front and rear suspensions are then developed in MapleSim. To avoid the computational complexity associated with introducing bushings or kinematic loops, all suspension linkages are lumped into a single unsprung mass at each corner of the vehicle. The SLEKQ models are designed to replicate the kinematic behaviour of a full suspension model using lookup tables or polynomial functions, which are obtained from the high-fidelity Adams model in this work. The predictive capability of each SLEKQ model relies on the use of appropriate parameters for the nonlinear spring and damper, which include the stiffness and damping contributions of the bushings, and the unsprung mass. Homotopy optimization is used to identify the parameters that minimize the difference between the responses of the Adams and MapleSim models. Finally, the SLEKQ models are assembled to construct a reduced 10-degree-of-freedom model of the full vehicle, the dynamic performance of which is validated against that of the high-fidelity Adams model using four-post heave and pitch tests.The authors gratefully acknowledge the financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the NSERC/Toyota/Maplesoft Industrial Research Chair program