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Shallow water equations are extensively considered in the domains of oceans, atmospheric modelling, and engineering research (Franca et al., 2022), which play significant roles in floods and tsunami governance. Nonetheless, the accurate…
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…
Conformal prediction is an uncertainty quantification method that constructs a prediction set for a previously unseen datum, ensuring the true label is included with a predetermined coverage probability. Adaptive conformal prediction has…
There is an increasing body of work exploring the integration of random projection into algorithms for numerical linear algebra. The primary motivation is to reduce the overall computational cost of processing large datasets. A suitably…
This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…
This paper describes a method for scheduling the events of a switched system to achieve an optimal performance. The approach has guarantees on convergence and computational complexity that parallel derivative-based iterative optimization…
We examine the problem of making reconciled forecasts of large collections of related time series through a behavioural/Bayesian lens. Our approach explicitly acknowledges and exploits the 'connectedness' of the series in terms of…
Some time series can be hierarchically organized into levels based on certain characteristics, such as geography or other attributes of interest. These series are referred to as hierarchical time series. Typically, forecasts are generated…
The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer these initial conditions…
Many natural systems exhibit chaotic behaviour such as the weather, hydrology, neuroscience and population dynamics. Although many chaotic systems can be described by relatively simple dynamical equations, characterizing these systems can…
In this paper, a new method was developed for initialising artificial neural networks predicting dynamics of time series. Initial weighting coefficients were determined for neurons analogously to the case of a linear prediction filter.…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…
Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…
Model Predictive Control is an extremely effective control method for systems with input and state constraints. Model Predictive Control performance heavily depends on the accuracy of the open-loop prediction. For systems with uncertainty…
We present results for long term and intermediate term prediction algorithms applied to a simple mechanical model of a fault. We use long term prediction methods based, for example, on the distribution of repeat times between large events…
This paper develops a novel change point identification method for high-dimensional data using random projections. By projecting high-dimensional time series into a one-dimensional space, we are able to leverage the rich literature for…
Reservoir computers can be used to predict time series generated by spatio-temporal chaotic systems. Using multiple reservoirs in parallel has shown improved performances for these predictions, by effectively reducing the input…
A popular approach for predicting the future of dynamical systems involves mapping them into a lower-dimensional "latent space" where prediction is easier. We show that the information-theoretically optimal approach uses different mappings…