Events

Date: 12 February 2026   Time: 14:00 - 15:00

Location: Hybrid: MB503, SMS, QMUL, or via the Teams link below

The state – i.e. "location" and "rate" – that a mechanistic system attains at a future time, is deterministically computable, given the state it is in now, since we know the potential function that causally connects any two states attained at two times, via Newton's 2nd Law. Following this argument, it appears that accurate forecasting of states of any generic deterministic dynamical system is possible, as long as we know the system potential that is in general, dependent on location and time. I will discuss my new forecasting method that advocates forecasting future states in such systems, by learning and forecasting the potential function, within a step-one-ahead forecasting approach. The process that generates the system state space variables, is modelled as locally stationary over an identified local time scale which we identify as a "time-window". Then in any time-window, the evolution of the density of such variables reduces to the Liouville equation, leading to the expression of this density as a function of integrals of motion. We introduce the sum of the potential function, and half the squared rate, as an integral that we refer to as "energy", to embed the sought potential in the support of the state space density, thereby allowing for information on the potential to percolate into the likelihood. This allows for inference on the potential function, (as well as the density) in any time-window, given the location values observed in this time-window. Thus, we can generate the training set that permits the learning of the location+time-dependent potential function, by modelling it as a sample function of a (high-dimensional) Gaussian Process. Then under extra guidance offered by an identified constraint, closed-form prediction of the potential is made at the next time point into the future, which in turn allows for the computation of the location and rate at that future time. I will present results of empirical illustrations of the method, towards forecasting COVID-19 daily infection numbers, as well as on forecasting crude oil price.

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