Spline-PINN: Approaching PDEs without Data Using Fast, Physics-Informed Hermite-Spline CNNs

Partial Differential Equations (PDEs) are notoriously difficult to solve. In general, closed form solutions are not available and numerical approximation schemes are computationally expensive. In this paper, we propose to approach the solution of PDEs based on a novel technique that combines the advantages of two recently emerging machine learning based approaches. First, physics-informed neural networks (PINNs) learn continuous solutions of PDEs and can be trained with little to no ground truth data. However, PINNs do not generalize well to unseen domains. Second, convolutional neural networks provide fast inference and generalize but either require large amounts of training data or a physics-constrained loss based on finite differences that can lead to inaccuracies and discretization artifacts. We leverage the advantages of both of these approaches by using Hermite spline kernels in order to continuously interpolate a grid-based state representation that can be handled by a CNN. This allows for training without any precomputed training data using a physics-informed loss function only and provides fast, continuous solutions that generalize to unseen domains. We demonstrate the potential of our method at the examples of the incompressible Navier-Stokes equation and the damped wave equation. Our models are able to learn several intriguing phenomena such as Karman vortex streets, the Magnus effect, Doppler effect, interference patterns and wave reflections. Our quantitative assessment and an interactive real-time demo show that we are narrowing the gap in accuracy of unsupervised ML based methods to industrial solvers for computational fluid dynamics (CFD) while being orders of magnitude faster

Cue-Signal-Response Analysis in 3D Chondrocyte Scaffolds with Anabolic Stimuli

Articular cartilage is an avascular connectivetissue responsible for bearing loads. Cell signaling plays acentral role in cartilage homeostasis and tissue engineering bydirecting chondrocytes to synthesize/degrade the extracellularmatrix or promote inflammatory responses. The aim ofthis paper was to investigate anabolic, catabolic and inflammatorypathways of well-known and underreported anabolicstimuli in 3D chondrocyte cultures and connect them todiverse cartilage responses including matrix regeneration andcell communication. A cue-signal-response experiment wasperformed in chondrocytes embedded in alginate scaffoldssubjected to a 9-day treatment with 7 anabolic cues. At thesignaling level diverse pathways were measured whereas atthe response level glycosaminoglycan (GAG) synthesis andcytokine releases were monitored. A significant increase ofGAG was observed for each stimulus and well knownanabolic phosphoproteins were activated. In addition,WNK1, an underreported protein of chondrocyte signaling,was uncovered. At the extracellular level, inflammatory andregulating cytokines were measured and DEFB1 andCXCL10 were identified as novel contributors to chondrocyteresponses, both closely linked to TLR signaling andinflammation. Finally, two new pro-growth factors with aninflammatory potential, Cadherin-11 and MGP wereobserved. Interestingly, well-known anabolic stimuli yieldedinflammatory responses which pinpoints to the pleiotropicroles of individual stimul

COMBSecretomics : a pragmatic methodological framework for higher-order drug combination analysis using secretomics

Multi drug treatments are increasingly used in the clinic to combat complex and co-occurring diseases. However, most drug combination discovery efforts today are mainly focused on anticancer therapy and rarely examine the potential of using more than two drugs simultaneously. Moreover, there is currently no reported methodology for performing second- and higher-order drug combination analysis of secretomic patterns, meaning protein concentration profiles released by the cells. Here, we introduce COMBSecretomics (https://github.com/EffieChantzi/COMBSecretomics.git), the first pragmatic methodological framework designed to search exhaustively for second- and higher-order mixtures of candidate treatments that can modify, or even reverse malfunctioning secretomic patterns of human cells. This framework comes with two novel model-free combination analysis methods; a tailor-made generalization of the highest single agent principle and a data mining approach based on top-down hierarchical clustering. Quality control procedures to eliminate outliers and non-parametric statistics to quantify uncertainty in the results obtained are also included. COMBSecretomics is based on a standardized reproducible format and could be employed with any experimental platform that provides the required protein release data. Its practical use and functionality are demonstrated by means of a proof-of-principle pharmacological study related to cartilage degradation. COMBSecretomics is the first methodological framework reported to enable secretome-related second- and higher-order drug combination analysis. It could be used in drug discovery and development projects, clinical practice, as well as basic biological understanding of the largely unexplored changes in cell-cell communication that occurs due to disease and/or associated pharmacological treatment conditions