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We present a new type of acquisition function for online decision-making in multi-armed and contextual bandit problems with extreme payoffs. Specifically, we model the payoff function as a Gaussian process and formulate a novel type of upper confidence bound acquisition function that guides exploration towards the bandits that are deemed most relevant according to the variability of the observed rewards. This is achieved by computing a tractable likelihood ratio that quantifies the importance of the output relative to the inputs and essentially acts as an attention mechanism that promotes exploration of extreme rewards. Our formulation is supported by asymptotic zero-regret guarantees, and its performance is demonstrated across several synthetic benchmarks, as well as two realistic examples involving noisy sensor network data. Finally, we provide a JAX library for efficient bandit optimization using Gaussian processes. [ABSTRACT FROM AUTHOR]

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj. [ABSTRACT FROM AUTHOR]

The peridynamic theory reformulates the equations of continuum mechanics in terms of integro-differential equations instead of partial differential equations. In this paper, we consider the construction of artificial boundary conditions (ABCs) for semi-discretized peridynamics using Green functions. Especially, the Green functions that represent the response to the single wave source are used to construct the accu2rate boundary conditions. The recursive relationships between the Green functions are proposed, therefore the Green functions can be computed through a differential and integral system with high precision. The numerical results demonstrate the accuracy of the proposed ABCs. The proposed method can be applied to modelling of wave propagation for other non-local theories and high-dimensional cases. [ABSTRACT FROM AUTHOR]