Scientific Meeting Friday 17 June

Wouter Edeling (Scientific Computing), Lisa Kohl (Cryptology)

13:00 - 13:30 Wouter Edeling (Scientific Computing), Small closure models for large multiscale problems

Turbulent flow problems are so-called multiscale problems, which comprise of a wide range of spatial and temporal scales. Computing all scales in a simulation is usually an insurmountable computational bottleneck. An engineering approach commonly involves a so-called coarse-graining
procedure, where only larger scales are computed directly, and the effect of the small scales enters the coarse-grained equations as an unknown forcing term, i.e. the subgrid-scale (SGS) term. Since the SGS term is unknown, it requires modelling. This is a complex modelling task, and despite the coarse-graining procedure, the forcing term still contains a high number unknown degrees of freedom. One could try to extract a model from data, and simultaneously decrease the number of unknowns by creating a Reduced-Order Model (ROM), for instance one based on extracting data-driven basis functions from available reference data. Instead of creating a ROM that aims to represent the full forcing term, we propose a new type of ROM that is tailor-made to capture spatially-integrated quantities of interest (QoIs). Examples of such QoIs include “climate-like statistics” of the full model, for instance the global energy or temperature of the system. We will show that if we restrict our interest to these small QoI, we can reduce the unknown degrees of freedom in the SGS term by several orders of magnitude.

13:30 - 14:00 Lisa Kohl (Cryptology), Compressed Sigma-Protocol Theory for Lattices

Σ-Protocols provide a well-understood and widely-used basis for zero-knowledge proofs, allowing a prover to convince a verifier that a committed vector satisfies a constraint C(x)=0 (captured by an arithmetic circuit) without revealing anything about the (typically long) input vector x, besides the veracity of the claim. Using ideas from secure multi-party computation and from so-called Bulletproofs, it has been shown that the communication of Σ-Protocols for proving general constraint-satisfiability problems can be compressed from linear to (poly)logarithmic in the input length, yielding so-called compressed Σ-protocols. In a recent work, which will be the focus of this talk, we present the first framework for compressed Σ-protocols that can be instantiated from lattice-based assumptions, thereby plausibly withstanding even quantum attacks.

This is joint work with Thomas Attema and Ronald Cramer.