Figure 1 An interesting Bayesian functional regression trick based on the so-called -exponential distribution: which has a special relationship with Besov spaces and so connects to functional inverse problems. It seems to be in the same family as elliptical process as per Bånkestad et al. (2020). NB, the -exponential distribution is not the Tsallis q-exponential distribution but rather one developed by Dashti, Harris, and Stuart (n.d.). Li, O’Connor, and Lan (2023): Regularization is one ...| The Dan MacKinlay stable of variably-well-consider’d enterprises
Normalising flows for PDE learning. Figure 1 Lipman et al. (2023) seems to be the origin point, extended by Kerrigan, Migliorini, and Smyth (2024) to function-valued PDEs. Figure 2: An illustration of our FFM method. The vector field (in black) transforms a noise sample drawn from a Gaussian process with a Matérn kernel (at ) to the function (at ) via solving a function space ODE. By sampling many such , we define a conditional path of measures approximately interpolating between and the f...| The Dan MacKinlay stable of variably-well-consider’d enterprises
Diffusion models for PDE learning. Figure 1 Slightly confusing terminology, because we are using diffusion models to learn PDEs, but the PDEs themselves are often used to model diffusion processes. Also sometimes the diffusion models that do the modelling aren’t actually diffusive, but are based on Poisson flow generative models. Naming things is hell. 1 Classical diffusion models TBD 2 Poisson Flow generative models These are based on non-diffusive physics but also seem to be used to simu...| The Dan MacKinlay stable of variably-well-consider’d enterprises
Figure 1 Placeholder. Levers for Biological Progress - by Niko McCarty In order for 50-100 years of biological progress to be condensed into 5-10 years of work, we’ll need to get much better at running experiments quickly and also collecting higher-quality datasets. This essay focuses on how we might do both, specifically for the cell. Though my focus in this essay is narrow — I don’t discuss bottlenecks in clinical trials, human disease, or animal testing — I hope others will take o...| The Dan MacKinlay stable of variably-well-consider’d enterprises