Task-oriented machine learning surrogates for tipping points of agent-based models.

We present a machine learning framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale approach, for the construction of different types of effective reduced order models from detailed agent-based simulators and the systematic multiscale numerical analysis of their emergent dynamics. The specific tasks of interest here include the detection of tipping points, and the uncertainty quantification of rare events near them. Our illustrative examples are an event-driven, stochastic financial market model describing the mimetic behavior of traders, and a compartmental stochastic epidemic model on an Erdös-Rényi network.

Parsimonious physics-informed random projection neural networks for initial value problems of ODEs and index-1 DAEs.

We present a numerical method based on random projections with Gaussian kernels and physics-informed neural networks for the numerical solution of initial value problems (IVPs) of nonlinear stiff ordinary differential equations (ODEs) and index-1 differential algebraic equations (DAEs), which may also arise from spatial discretization of partial differential equations (PDEs). The internal weights are fixed to ones while the unknown weights between the hidden and output layer are computed with Newton's iterations using the Moore-Penrose pseudo-inverse for low to medium scale and sparse QR decomposition with L 2 regularization for medium- to large-scale systems. Building on previous works on random projections, we also prove its approximation accuracy.