Jan-Philipp von Bassewitz

Jan-Philipp von Bassewitz, Sebastian Kaltenbach, Petros Koumoutsakos

Reliable predictions of critical phenomena, such as weather, wildfires and epidemics often rely on models described by Partial Differential Equations (PDEs). However, simulations that capture the full range of spatio-temporal scales described by such PDEs are often prohibitively expensive. Consequently, coarse-grained simulations are usually deployed that adopt various heuristics and empirical closure terms to account for the missing information. We propose a novel and systematic approach for identifying closures in under-resolved PDEs using grid-based Reinforcement Learning. This formulation incorporates inductive bias and exploits locality by deploying a central policy represented efficiently by a Fully Convolutional Network (FCN). We demonstrate the capabilities and limitations of our framework through numerical solutions of the advection equation and the Burgers' equation. Our results show accurate predictions for in- and out-of-distribution test cases as well as a significant speedup compared to resolving all scales.

Jan-Philipp von Bassewitz, Adeel Pervez, Marco Fumero et al.

Modeling the dynamics of cellular differentiation is fundamental to advancing the understanding and treatment of diseases associated with this process, such as cancer. With the rapid growth of single-cell datasets, this has also become a particularly promising and active domain for machine learning. Current state-of-the-art models, however, rely on computationally expensive optimal transport preprocessing and multi-stage training, while also not discovering explicit gene interactions. To address these challenges we propose Cell-Mechanistic Neural Networks (Cell-MNN), an encoder-decoder architecture whose latent representation is a locally linearized ODE governing the dynamics of cellular evolution from stem to tissue cells. Cell-MNN is fully end-to-end (besides a standard PCA pre-processing) and its ODE representation explicitly learns biologically consistent and interpretable gene interactions. Empirically, we show that Cell-MNN achieves competitive performance on single-cell benchmarks, surpasses state-of-the-art baselines in scaling to larger datasets and joint training across multiple datasets, while also learning interpretable gene interactions that we validate against the TRRUST database of gene interactions.