Over forty years ago average-case error was proposed in the applied mathematics literature
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …

Information field theory (IFT), the information theory for fields, is a mathematical framework
for signal reconstruction and non-parametric inverse problems. Artificial intelligence (AI) and …

Reputation is a central element of social communications, be it with human or artificial
intelligence (AI), and as such can be the primary target of malicious communication …

Knowledge on evolving physical fields is of paramount importance in science, technology,
and economics. Dynamical field inference (DFI) addresses the problem of reconstructing a …

We explore a new simulation scheme for partial differential equations (PDE's) called
information field dynamics (IFD). Information field dynamics is a probabilistic numerics …

Computer simulations of differential equations require a time discretization, which inhibits to
identify the exact solution with certainty. Probabilistic simulations take this into account via …

Communication is a cornerstone of social interactions, be it with human or artificial
intelligence (AI). Yet it can be harmful, depending on the honesty of the exchanged …

Physics is about building a model of the world. Building a model can have two different
interpretations. On the one hand, it can refer to the construction of a model that mimics the …