Andrea Papini

Annika Lang, Andrea Papini, Verena Schwarz

The stochastic heat equation on the sphere driven by an additive square-integra\-ble Lévy process is approximated by a spectral method in space and forward and backward Euler--Maruyama schemes in time. New regularity results are proven for its solution. The spectral approximation is based on a truncation of the series expansion with respect to the spherical harmonic functions. For a given regularity of the initial condition and two different settings of regularity for the driving noise, strong convergence rates for the spectral approximation and for the Euler--Maruyama methods are proven. Moreover, weak rates of up to twice the strong rates are shown. Numerical simulations confirm the theoretical results.

Carlo Metta, Marco Fantozzi, Andrea Papini et al.

We introduce a novel computational unit for neural networks that features multiple biases, challenging the traditional perceptron structure. This unit emphasizes the importance of preserving uncorrupted information as it is passed from one unit to the next, applying activation functions later in the process with specialized biases for each unit. Through both empirical and theoretical analyses, we show that by focusing on increasing biases rather than weights, there is potential for significant enhancement in a neural network model's performance. This approach offers an alternative perspective on optimizing information flow within neural networks. See source code at https://github.com/CuriosAI/dac-dev.

Carlo Metta, Marco Gregnanin, Andrea Papini et al.

This paper presents the second-place methodology in the Volvo Discovery Challenge at ECML-PKDD 2024, where we used Long Short-Term Memory networks and pseudo-labeling to predict maintenance needs for a component of Volvo trucks. We processed the training data to mirror the test set structure and applied a base LSTM model to label the test data iteratively. This approach refined our model's predictive capabilities and culminated in a macro-average F1-score of 0.879, demonstrating robust performance in predictive maintenance. This work provides valuable insights for applying machine learning techniques effectively in industrial settings.

David Cohen, Björn Müller, Andrea Papini

We investigate the long-time behavior of exact solutions and numerical approximations of linear stochastic evolution equations defined on the sphere. We focus on three classical models arising in mathematical physics: the stochastic wave equation, the stochastic Schrödinger equation, and the stochastic Maxwell's equations. For these SPDEs, we analyze several widely used time integrators with respect to trace formulas describing the evolution of physically relevant quantities such as energy, mass, and momentum dependent on the forcing term. In particular, we prove that the forward and backward Euler-Maruyama schemes fail to reproduce the correct long-time behavior of the exact solutions. In addition, we prove that the stochastic exponential integrator preserves the correct long-time behavior of the physical quantities of interest. Finally, several numerical experiments are provided to illustrate our theoretical findings.