Michael McLaughlin

Victor DeCaria, Traian Iliescu, William Layton et al.

We propose a novel artificial compression, reduced order model (AC-ROM) for the numerical simulation of viscous incompressible fluid flows. The new AC-ROM provides approximations not only for velocity, but also for pressure, which is needed to calculate forces on bodies in the flow and to connect the simulation parameters with pressure data. The new AC-ROM does not require that the velocity-pressure ROM spaces satisfy the inf-sup (Ladyzhenskaya-Babuska-Brezzi) condition and its basis functions are constructed from data that are not required to be weakly-divergence free. We prove error estimates for the reduced basis discretization of the AC-ROM. We also investigate numerically the new AC-ROM in the simulation of a two-dimensional flow between offset cylinders.

Tatiana Chakravorti, Robert Fraleigh, Timothy Fritton et al.

We present a prototype hybrid prediction market and demonstrate the avenue it represents for meaningful human-AI collaboration. We build on prior work proposing artificial prediction markets as a novel machine-learning algorithm. In an artificial prediction market, trained AI agents buy and sell outcomes of future events. Classification decisions can be framed as outcomes of future events, and accordingly, the price of an asset corresponding to a given classification outcome can be taken as a proxy for the confidence of the system in that decision. By embedding human participants in these markets alongside bot traders, we can bring together insights from both. In this paper, we detail pilot studies with prototype hybrid markets for the prediction of replication study outcomes. We highlight challenges and opportunities, share insights from semi-structured interviews with hybrid market participants, and outline a vision for ongoing and future work.

Joseph A. Fiordilino, Michael McLaughlin

Ensemble calculations are essential for systems with uncertain data but require substantial increase in computational resources. This increase severely limits ensemble size. To reach beyond current limits, we present a first-order artificial compressibility ensemble algorithm. This algorithm effectively decouples the velocity and pressure solve via artificial compression, thereby reducing computational complexity and execution time. Further reductions in storage and computation time are achieved via a splitting of the convective term. Nonlinear energy stability and first-order convergence of the method are proven under a CFL-type condition involving fluctuations of the velocity. Numerical tests are provided which confirm the theoretical analyses and illustrate the value of ensemble calculations.

Sarah Rajtmajer, Christopher Griffin, Jian Wu et al.

Explainably estimating confidence in published scholarly work offers opportunity for faster and more robust scientific progress. We develop a synthetic prediction market to assess the credibility of published claims in the social and behavioral sciences literature. We demonstrate our system and detail our findings using a collection of known replication projects. We suggest that this work lays the foundation for a research agenda that creatively uses AI for peer review.

Robin Ming Chen, William Layton, Michael McLaughlin

A standard artificial compression (AC) method for incompressible flow is $$ \frac{u_{n+1}^{\varepsilon }-u_{n}^{\varepsilon }}{k}+u_{n+1}^{\varepsilon }\cdot \nabla u_{n+1}^{\varepsilon }+{\frac{1}{2}}u_{n+1}^{\varepsilon }\nabla \cdot u_{n+1}^{\varepsilon }+\nabla p_{n+1}^{\varepsilon }-νΔu_{n+1}^{\varepsilon }=f\text{ ,} \\ \varepsilon \frac{p_{n+1}^{\varepsilon }-p_{n}^{\varepsilon }}{k} +\nabla \cdot u_{n+1}^{\varepsilon }=0 $$ for, typically, $\varepsilon =k$ (timestep). It is fast, efficient and stable with accuracy $O(\varepsilon +k)$. For adaptive (and thus variable) timestep $k_{n}$ (and thus $\varepsilon =\varepsilon _{n}$) its long time stability is unknown. For variable $k,\varepsilon $ this report shows how to adapt a standard AC method to recover a provably stable method. For the associated continuum AC model, we prove convergence of the $\varepsilon =\varepsilon (t)$\ artificial compression model to a weak solution of the incompressible Navier-Stokes equations as $\varepsilon =\varepsilon (t)\rightarrow 0$. The analysis is based on space-time Strichartz estimates for a non-autonomous acoustic equation. Variable $\varepsilon ,k$ numerical tests in $2d$ and $3d$ are given for the new AC method.