1,720,969 research outputs found
PTPI-DL-ROMs: Pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs
No full textAmong several recently proposed data-driven Reduced Order Models (ROMs), the coupling of Proper Orthogonal Decompositions (POD) and deep learning-based ROMs (DL-ROMs) has proved to be a successful strategy to construct non-intrusive, highly accurate, surrogates for the real time solution of parametric nonlinear time-dependent PDEs. Inexpensive to evaluate, POD-DL-ROMs are also relatively fast to train, thanks to their limited complexity. However, POD-DL-ROMs account for the physical laws governing the problem at hand only through the training data, that are usually obtained through a full order model (FOM) relying on a highfidelity discretization of the underlying equations. Moreover, the accuracy of POD-DL-ROMs strongly depends on the amount of available data. In this paper, we consider a major extension of POD-DL-ROMs by enforcing the fulfillment of the governing physical laws in the training process - that is, by making them physics-informed - to compensate for possible scarce and/or unavailable data and improve the overall reliability. To do that, we first complement POD-DLROMs with a trunk net architecture, endowing them with the ability to compute the problem's solution at every point in the spatial domain, and ultimately enabling a seamless computation of the physics-based loss by means of the strong continuous formulation. Then, we introduce an efficient training strategy that limits the notorious computational burden entailed by a physics-informed training phase. In particular, we take advantage of the few available data to develop a low-cost pre-training procedure; then, we fine-tune the architecture in order to further improve the prediction reliability. Accuracy and efficiency of the resulting pre-trained physics-informed DL-ROMs (PTPI-DL-ROMs) are then assessed on a set of test cases ranging from non-affinely parametrized advection-diffusion-reaction equations, to nonlinear problems like the Navier-Stokes equations for fluid flows
Handling geometrical variability in nonlinear reduced order modeling through Continuous Geometry-Aware DL-ROMs
No full textDeep Learning-based Reduced Order Models (DL-ROMs) provide nowadays a well-established class of accurate surrogate models for complex physical systems described by parameterised PDEs, by nonlinearly compressing the solution manifold into a handful of latent coordinates. Until now, design and application of DL-ROMs mainly focused on physically parameterised problems. Within this work, we provide a novel extension of these architectures to problems featuring geometrical variability and parameterised domains, namely, we propose Continuous Geometry-Aware DL-ROMs (CGA-DL-ROMs). In particular, the space-continuous nature of the proposed architecture matches the need to deal with multi-resolution datasets, which are quite common in the case of geometrically parameterised problems. Moreover, CGA-DL-ROMs are endowed with a strong inductive bias that makes them aware of geometrical parametrizations, thus enhancing both the compression capability and the overall performance of the architecture. Within this work, we justify our findings through a thorough theoretical analysis, and we practically validate our claims by means of a series of numerical tests encompassing physically-and-geometrically parameterised PDEs, ranging from the unsteady Navier–Stokes equations for fluid dynamics to advection–diffusion–reaction equations for mathematical biology
Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition
No full textPOD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality reduction obtained through proper orthogonal decomposition (POD) for the sake of efficiency, (ii) an autoencoder architecture that further reduces the dimensionality of the POD space to a handful of latent coordinates, and (iii) a dense neural network to learn the map that describes the dynamics of the latent coordinates as a function of the input parameters and the time variable. Within this work, we aim at justifying the outstanding approximation capabilities of POD-DL-ROMs by means of a thorough error analysis, showing how the sampling required to generate training data, the dimension of the POD space, and the complexity of the underlying neural networks, impact on the solutions us to formulate practical criteria to control the relative error in the approximation of the solution field of interest, and derive general error estimates. Furthermore, we show that, from a theoretical point of view, POD-DL-ROMs outperform several deep learning-based techniques in terms of model complexity. Finally, we validate our findings by means of suitable numerical experiments, ranging from parameter-dependent operators analytically defined to several parametrized PDEs
On latent dynamics learning in nonlinear reduced order modeling
No full textIn this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality reduction problem, while constraining the latent state to evolve accordingly to an unknown dynamical system. A time-continuous setting is employed to derive error and stability estimates for the LDM approximation of the full order model (FOM) solution. We analyze the impact of using an explicit Runge-Kutta scheme in the time-discrete setting, resulting in the 4 LDM formulation, and further explore the learnable setting, 4LDM theta, where deep neural networks approximate the discrete LDM components, while providing a bounded approximation error with respect to the FOM. Moreover, we extend the concept of parameterized Neural ODE - a possible way to build data-driven dynamical systems with varying input parameters - to be a convolutional architecture, where the input parameters information is injected by means of an affine modulation mechanism, while designing a convolutional autoencoder neural network able to retain spatial- coherence, thus enhancing interpretability at the latent level. Numerical experiments, including the Burgers' and the advection-diffusion-reaction equations, demonstrate the framework's ability to obtain a time-continuous approximation of the FOM solution, thus being able to query the LDM approximation at any given time instance while retaining a prescribed level of accuracy. Our findings highlight the remarkable potential of the proposed LDMs, representing a mathematically rigorous framework to enhance the accuracy and approximation capabilities of reduced order modeling for time-dependent parameterized PDEs
Tumor reactive stroma in cholangiocarcinoma: The fuel behind cancer aggressiveness
No full textCholangiocarcinoma (CCA) is a highly aggressive epithelial malignancy still carrying a dismal prognosis, owing to early lymph node metastatic dissemination and striking resistance to conventional chemotherapy. Although mechanisms underpinning CCA progression are still a conundrum, it is now increasingly recognized that the desmoplastic microenvironment developing in conjunction with biliary carcinogenesis, recently renamed tumor reactive stroma (TRS), behaves as a paramount tumor-promoting driver. Indeed, once being recruited, activated and dangerously co-opted by neoplastic cells, the cellular components of the TRS (myofibroblasts, macrophages, endothelial cells and mesenchymal stem cells) continuously rekindle malignancy by secreting a huge variety of soluble factors (cyto/chemokines, growth factors, morphogens and proteinases). Furthermore, these factors are long-term stored within an abnormally remodeled extracellular matrix (ECM), which in turn can deleteriously mold cancer cell behavior. In this review, we will highlight evidence for the active role played by reactive stromal cells (as well as by the TRS-associated ECM) in CCA progression, including an overview of the most relevant TRS-derived signals possibly fueling CCA cell aggressiveness. Hopefully, a deeper knowledge of the paracrine communications reciprocally exchanged between cancer and stromal cells will steer the development of innovative, combinatorial therapies, which can finally hinder the progression of CCA, as well as of other cancer types with abundant TRS, such as pancreatic and breast carcinomas
Molecular mechanisms driving cholangiocarcinoma invasiveness: An overview
No full textThe acquisition of invasive functions by tumor cells is a first and crucial step toward the development of metastasis, which nowadays represents the main cause of cancer-related death. Cholangiocarcinoma (CCA), a primary liver cancer originating from the biliary epithelium, typically develops intrahepatic or lymph node metastases at early stages, thus preventing the majority of patients from undergoing curative treatments, consistent with their very poor prognosis. As in most carcinomas, CCA cells gradually adopt a motile, mesenchymal-like phenotype, enabling them to cross the basement membrane, detach from the primary tumor, and invade the surrounding stroma. Unfortunately, little is known about the molecular mechanisms that synergistically orchestrate this proinvasive phenotypic switch. Autocrine and paracrine signals (cyto/chemokines, growth factors, and morphogens) permeating the tumor microenvironment undoubtedly play a prominent role in this context. Moreover, a number of recently identified signaling systems are currently drawing attention as putative mechanistic determinants of CCA cell invasion. They encompass transcription factors, protein kinases and phosphatases, ubiquitin ligases, adaptor proteins, and miRNAs, whose aberrant expression may result from either stochastic mutations or the abnormal activation of upstream pro-oncogenic pathways. Herein we sought to summarize the most relevant molecules in this field and to discuss their mechanism of action and potential prognostic relevance in CCA. Hopefully, a deeper knowledge of the molecular determinants of CCA invasiveness will help to identify clinically useful biomarkers and novel druggable targets, with the ultimate goal to develop innovative approaches to the management of this devastating malignancy
Revisiting Epithelial-to-Mesenchymal Transition in Liver Fibrosis: Clues for a Better Understanding of the "reactive" Biliary Epithelial Phenotype
Full text linkWhether liver epithelial cells contribute to the development of hepatic scarring by undergoing epithelial-to-mesenchymal transition (EMT) is a controversial issue. Herein, we revisit the concept of EMT in cholangiopathies, a group of severe hepatic disorders primarily targeting the bile duct epithelial cell (cholangiocyte), leading to progressive portal fibrosis, the main determinant of liver disease progression. Unfortunately, therapies able to halt this process are currently lacking. In cholangiopathies, fibrogenesis is part of ductular reaction, a reparative complex involving epithelial, mesenchymal, and inflammatory cells. Ductular reactive cells (DRC) are cholangiocytes derived from the activation of the hepatic progenitor cell compartment. These cells are arranged into irregular strings and express a "reactive" phenotype, which enables them to extensively crosstalk with the other components of ductular reaction. We will first discuss EMT in liver morphogenesis and then highlight how some of these developmental programs are partly reactivated in DRC. Evidence for "bona fide" EMT changes in cholangiocytes is lacking, but expression of some mesenchymal markers represents a fundamental repair mechanism in response to chronic biliary damage with potential harmful fibrogenetic effects. Understanding microenvironmental cues and signaling perturbations promoting these changes in DRC may help to identify potential targets for new antifibrotic therapies in cholangiopathies
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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