DiTTO: Diffusion-inspired Temporal Transformer Operator

Solving partial differential equations (PDEs) using a data-driven approach has become increasingly common. The recent development of the operator learning paradigm has enabled the solution of a broader range of PDE-related problems. We propose an operator learning method to solve time-dependent PDEs continuously in time without needing any temporal discretization. The proposed approach, named DiTTO, is inspired by latent diffusion models. While diffusion models are usually used in generative artificial intelligence tasks, their time-conditioning mechanism is extremely useful for PDEs. The diffusion-inspired framework is combined with elements from the Transformer architecture to improve its capabilities. We demonstrate the effectiveness of the new approach on a wide variety of PDEs in multiple dimensions, namely the 1-D Burgers' equation, 2-D Navier-Stokes equations, and the acoustic wave equation in 2-D and 3-D. DiTTO achieves state-of-the-art results in terms of accuracy for these problems. We also present a method to improve the performance of DiTTO by using fast sampling concepts from diffusion models. Finally, we show that DiTTO can accurately perform zero-shot super-resolution in time

Understanding the Efficacy of U-Net & Vision Transformer for Groundwater Numerical Modelling

This paper presents a comprehensive comparison of various machine learning models, namely U-Net, U-Net integrated with Vision Transformers (ViT), and Fourier Neural Operator (FNO), for time-dependent forward modelling in groundwater systems. Through testing on synthetic datasets, it is demonstrated that U-Net and U-Net + ViT models outperform FNO in accuracy and efficiency, especially in sparse data scenarios. These findings underscore the potential of U-Net-based models for groundwater modelling in real-world applications where data scarcity is prevalent

Targeting of prion-infected lymphoid cells to the central nervous system accelerates prion infection

BACKGROUND: Prions, composed of a misfolded protein designated PrP(Sc), are infectious agents causing fatal neurodegenerative diseases. We have shown previously that, following induction of experimental autoimmune encephalomyelitis, prion-infected mice succumb to disease significantly earlier than controls, concomitant with the deposition of PrP(Sc) aggregates in inflamed white matter areas. In the present work, we asked whether prion disease acceleration by experimental autoimmune encephalomyelitis results from infiltration of viable prion-infected immune cells into the central nervous system. METHODS: C57Bl/6 J mice underwent intraperitoneal inoculation with scrapie brain homogenates and were later induced with experimental autoimmune encephalomyelitis by inoculation of MOG(35-55) in complete Freund's adjuvant supplemented with pertussis toxin. Spleen and lymph node cells from the co-induced animals were reactivated and subsequently injected into naïve mice as viable cells or as cell homogenates. Control groups were infected with viable and homogenized scrapie immune cells only with complete Freund's adjuvant. Prion disease incubation times as well as levels and sites of PrP(Sc) deposition were next evaluated. RESULTS: We first show that acceleration of prion disease by experimental autoimmune encephalomyelitis requires the presence of high levels of spleen PrP(Sc). Next, we present evidence that mice infected with activated prion-experimental autoimmune encephalomyelitis viable cells succumb to prion disease considerably faster than do mice infected with equivalent cell extracts or other controls, concomitant with the deposition of PrP(Sc) aggregates in white matter areas in brains and spinal cords. CONCLUSIONS: Our results indicate that inflammatory targeting of viable prion-infected immune cells to the central nervous system accelerates prion disease propagation. We also show that in the absence of such targeting it is the load of PrP(Sc) in the inoculum that determines the infectivity titers for subsequent transmissions. Both of these conclusions have important clinical implications as related to the risk of prion disease contamination of blood products

A Convolutional Dispersion Relation Preserving Scheme for the Acoustic Wave Equation

We propose an accurate numerical scheme for approximating the solution of the two dimensional acoustic wave problem. We use machine learning to find a stencil suitable even in the presence of high wavenumbers. The proposed scheme incorporates physically informed elements from the field of optimized numerical schemes into a convolutional optimization machine learning algorithm

Fatal Neurological Disease in Scrapie-Infected Mice Induced for Experimental Autoimmune Encephalomyelitis▿

During the years or decades of prion disease incubation, at-risk individuals are certain to encounter diverse pathological insults, such as viral and bacterial infections, autoimmune diseases, or inflammatory processes. Whether prion disease incubation time and clinical signs or otherwise the pathology of intercurrent diseases can be affected by the coinfection process is unknown. To investigate this possibility, mice infected with the scrapie agent at both high and low titers were subsequently induced for experimental autoimmune encephalomyelitis, an immune system-mediated model of central nervous system (CNS) inflammation. We show here that coinduced mice died from a progressive neurological disease long before control mice succumbed to classical scrapie. To investigate the mechanism of the coinduced syndrome, we evaluated biochemical and pathological markers of both diseases. Brain and spleen PrPSc levels in the dying coinduced mice were comparable to those observed in asymptomatic scrapie-infected animals, suggesting that coinduced disease is not an accelerated form of scrapie. In contrast, inflammatory markers, such as demyelination, immune cell infiltrates, and gliosis, were markedly increased in coinduced mouse spinal cords. Activated astrocytes were especially elevated in the medulla oblongata. Furthermore, PrPsc depositions were found in demyelinated white matter areas in coinduced mouse spinal cords, suggesting the presence of activated infected immune cells that infiltrate into the CNS to facilitate the process of prion neuroinvasion. We hypothesize that inflammatory processes affecting the CNS may have severe clinical implications in subjects incubating prion diseases

Differential Expression of Prokineticin Receptors by Endothelial Cells Derived from Different Vascular Beds: a Physiological Basis for Distinct Endothelial Function

International audienceProkineticins (PKs), multifunctional secreted proteins, activate two endogenous G protein-coupled receptors (R) termed PK-R1 and PK-R2. It was suggested that PK1 acts selectively on the endothelium of endocrine glands, yet PK-Rs were also found in endothelial cells (EC) derived from other tissues. Therefore we examined here the characteristics of PK - system in EC derived from different vascular beds. Corpus luteum (CL)-derived EC (LEC) expressed both PK-R1 and PK-R2. In contrast, EC from the aorta (BAEC) only expressed PK-R1. Interestingly, also EC from brain capillaries (BCEC) expressed only PK-R1. The distinct pattern of PK-R expression may define EC phenotypic heterogeneity. Regulation of receptor expression also differed in BAEC and LEC: TNFalpha markedly reduced PK-R1 only in BAEC, but serum removal decreased PK-R1 in both cell types. Therefore, if cells were initially serum-starved, the anti-apoptotic effect of PKs was retained only in LEC. Yet, addition of PKs concomitant with serum removal enhanced the proliferation and survival of both BAEC and LEC. Immunohistochemical staining showed that in CL and aorta PK1 was expressed in smooth muscle cells in vessel walls, suggesting a paracrine mode of action. PK1 enhanced the net paracellular transport (measured by electrical resistance and Mannitol transport) in LEC but not in BAEC or BCEC. Collectively, these findings indicate that PKs serve as mitogens and survival factors for microvascular (LEC) and macrovascular (BAEC) EC. However, the distinct expression and function of PK receptors suggest different physiological roles for these receptors in various EC types