  Extreme events in society and nature, such as pandemic spikes, rogue waves,
or structural failures, can have catastrophic consequences. Characterizing
extremes is difficult as they occur rarely, arise from seemingly benign
conditions, and belong to complex and often unknown infinite-dimensional
systems. Such challenges render attempts at characterizing them as moot. We
address each of these difficulties by combining novel training schemes in
Bayesian experimental design (BED) with an ensemble of deep neural operators
(DNOs). This model-agnostic framework pairs a BED scheme that actively selects
data for quantifying extreme events with an ensemble of DNOs that approximate
infinite-dimensional nonlinear operators. We find that not only does this
framework clearly beat Gaussian processes (GPs) but that 1) shallow ensembles
of just two members perform best; 2) extremes are uncovered regardless of the
state of initial data (i.e. with or without extremes); 3) our method eliminates
"double-descent" phenomena; 4) the use of batches of suboptimal acquisition
points compared to step-by-step global optima does not hinder BED performance;
and 5) Monte Carlo acquisition outperforms standard optimizers in
high-dimensions. Together these conclusions form the foundation of an
AI-assisted experimental infrastructure that can efficiently infer and pinpoint
critical situations across many domains, from physical to societal systems.
