Predicting the Future: Completing Models of Observed Complex Systems
Through the development of an exact path integral for use in transferring information from observations to a model of the observed system, the author provides a general framework for the discussion of model building and evaluation across disciplines. Through many illustrative examples drawn from models in neuroscience, geosciences, and nonlinear electrical circuits, the concepts are exemplified in detail. Practical numerical methods for approximate evaluations of the path integral are explored, and their use in designing experiments and determining a model’s consistency with observations is explored.
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Abarbanel 1996 accurate estimation action approximation assimilation path integral assimilation window attractor biophysical calculation channels chaotic CLEs Colpitts oscillator completed model Complex Systems conditional mutual information cost function coupling data assimilation path deterministic differential equations discussion display dynamical equations dynamical system Epoch 19 estimated parameters evaluated example expected value experimental expŒA0.X fixed parameters flow formulation gating variables Gaussian initial conditions injected current IPOPT kurtosis Langevin equation Lorenz96 model Lyapunov exponents Markov measurement functions membrane voltage methods minima model equations model output Monte Carlo Monte Carlo methods mutual information NaKL model NaKLh neuron model noise nonlinear observation window orbits Panel physical prediction window presented probability distribution problem procedure quantities RMS error selected shallow water equations space Springer Science+Business Media statistical data assimilation stimulus synchronization error synchronization manifold trajectories twin experiment unobserved state variables voltage response waterwheel