Thermodynamics-informed neural networks for physically realistic mixed reality

The imminent impact of immersive technologies in society urges for active research in real-time and interactive physics simulation for virtual worlds to be realistic. In this context, realistic means to be compliant to the laws of physics. In this paper we present a method for computing the dynamic response of (possibly non-linear and dissipative) deformable objects induced by real-time user interactions in mixed reality using deep learning. The graph-based architecture of the method ensures the thermodynamic consistency of the predictions, whereas the visualization pipeline allows a natural and realistic user experience. Two examples of virtual solids interacting with virtual or physical solids in mixed reality scenarios are provided to prove the performance of the method

Manifold learning for coherent design interpolation based on geometrical and topological descriptors

In the context of intellectual property in the manufacturing industry, know-how is referred to practical knowledge on how to accomplish a specific task. This know-how is often difficult to be synthesised in a set of rules or steps as it remains in the intuition and expertise of engineers, designers, and other professionals. Today, a new research line in this concern spot-up thanks to the explosion of Artificial Intelligence and Machine Learning algorithms and its alliance with Computational Mechanics and Optimisation tools. However, a key aspect with industrial design is the scarcity of available data, making it problematic to rely on deep-learning approaches. Assuming that the existing designs live in a manifold, in this paper, we propose a synergistic use of existing Machine Learning tools to infer a reduced manifold from the existing limited set of designs and, then, to use it to interpolate between the individuals, working as a generator basis, to create new and coherent designs. For this, a key aspect is to be able to properly interpolate in the reduced manifold, which requires a proper clustering of the individuals. From our experience, due to the scarcity of data, adding topological descriptors to geometrical ones considerably improves the quality of the clustering. Thus, a distance, mixing topology and geometry is proposed. This distance is used both, for the clustering and for the interpolation. For the interpolation, relying on optimal transport appear to be mandatory. Examples of growing complexity are proposed to illustrate the goodness of the method

Hybrid Twin in Complex System Settings

Los beneficios de un conocimiento profundo de los procesos tecnológicos e industriales de nuestro mundo son incuestionables. La optimización, el análisis inverso o el control basado en la simulación son algunos de los procedimientos que pueden llevarse a cabo una vez que los conocimientos anteriores se transforman en valor para las empresas. Con ello se consiguen mejores tecnologías que acaban beneficiando enormemente a la sociedad. Pensemos en una actividad rutinaria para muchas personas hoy en día, como coger un avión. Todos los procedimientos anteriores se llevan a cabo en el diseño del avión, en el control a bordo y en el mantenimiento, lo que culmina en un producto tecnológicamente eficiente en cuanto a recursos. Este alto valor añadido es lo que está impulsando a la Ciencia de la Ingeniería Basada en la Simulación (Simulation Based Engineering Science, SBES) a introducir importantes mejoras en estos procedimientos, lo que ha supuesto avances importantes en una gran variedad de sectores como la sanidad, las telecomunicaciones o la ingeniería.Sin embargo, la SBES se enfrenta actualmente a varias dificultades para proporcionar resultados precisos en escenarios industriales complejos. Una de ellas es el elevado coste computacional asociado a muchos problemas industriales, que limita seriamente o incluso inhabilita los procesos clave descritos anteriormente. Otro problema es que, en otras aplicaciones, los modelos más precisos (que a su vez son los más caros computacionalmente) no son capaces de tener en cuenta todos los detalles que rigen el sistema físico estudiado, con desviaciones observadas que parecen escapar de nuestro conocimiento.Por lo tanto, en este contexto, a lo largo de este manuscrito se proponen novedosas estrategias y técnicas numéricas para hacer frente a los retos a los que se enfrenta la SBES. Para ello, se analizan diferentes aplicaciones industriales.El panorama anterior junto con el exhaustivo desarrollo producido en la Ciencia de Datos, brinda además una oportunidad perfecta para los denominados Dynamic Data Driven Application Systems (DDDAS), cuyo objetivo principal es fusionar los algoritmos clásicos de simulación con los datos procedentes de medidas experimentales. En este escenario, los datos y las simulaciones ya no estarían desacoplados, sino que formarían una relación simbiótica que alcanzaría hitos inconcebibles hasta estos días. Más en detalle, los datos ya no se entenderán como una calibración estática de un determinado modelo constitutivo, sino que el modelo se corregirá dinámicamente tan pronto como los datos experimentales y las simulaciones tiendan a diverger.Por esta razón, la presente tesis ha hecho especial énfasis en las técnicas de reducción de modelos, ya que no sólo son una herramienta para reducir la complejidad computacional, sino también un elemento clave para cumplir con las restricciones de tiempo real que surgen del marco de los DDDAS.Además, esta tesis presenta nuevas metodologías basadas en datos para enriquecer el denominado paradigma Hybrid Twin. Un paradigma cuya motivación radica en su habilidad de posibilitar los DDDAS. ¿Cómo? combinando soluciones paramétricas y técnicas de reducción de modelos con correcciones dinámicas generadas “al vuelo'' basadas en los datos experimentales recogidos en cada instante.<br /

A thermodynamics-informed active learning approach to perception and reasoning about fluids

Learning and reasoning about physical phenomena is still a challenge in robotics development, and computational sciences play a capital role in the search for accurate methods able to provide explanations for past events and rigorous forecasts of future situations. We propose a thermodynamics-informed active learning strategy for fluid perception and reasoning from observations. As a model problem, we take the sloshing phenomena of different fluids contained in a glass. Starting from full-field and high-resolution synthetic data for a particular fluid, we develop a method for the tracking (perception) and simulation (reasoning) of any previously unseen liquid whose free surface is observed with a commodity camera. This approach demonstrates the importance of physics and knowledge not only in data-driven (gray-box) modeling but also in real-physics adaptation in low-data regimes and partial observations of the dynamics. The presented method is extensible to other domains such as the development of cognitive digital twins able to learn from observation of phenomena for which they have not been trained explicitly

Tensor representation of non-linear models using cross approximations

This is a post-peer-review, pre-copyedit version of an article published in Journal of scientific computing. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10915-019-00917-2Tensor representations allow compact storage and efficient manipulation of multi-dimensional data. Based on these, tensor methods build low-rank subspaces for the solution of multi-dimensional and multi-parametric models. However, tensor methods cannot always be implemented efficiently, specially when dealing with non-linear models. In this paper, we discuss the importance of achieving a tensor representation of the model itself for the efficiency of tensor-based algorithms. We investigate the adequacy of interpolation rather than projection-based approaches as a means to enforce such tensor representation, and propose the use of cross approximations for models in moderate dimension. Finally, linearization of tensor problems is analyzed and several strategies for the tensor subspace construction are proposed.Peer ReviewedPostprint (author's final draft

The Proper Generalized Decomposition (PGD) as a numerical procedure to solve 3D cracked plates in linear elastic fracture mechanics

In this work, we present a new approach to solve linear elastic crack problems in plates using the so-called Proper Generalized Decomposition (PGD). In contrast to the standard FE method, the method enables to solve the crack problem in an efficient way by obtaining a single solution in which the Poisson's ratio v and the plate thickness B are non-fixed parameters. This permits to analyze the influence of v and B in the 3D solutions at roughly the cost of a series expansion of 2D analyses. Computationally, the PGD solution is less expensive than a full 3D standard FE analysis for typical discretizations used in practice to capture singularities in 3D crack problems. In order to verify the effectiveness of the proposed approach, the method is applied to cracked plates in mode I with a straight-through crack and a quarter-elliptical corner crack, validating J-integral results with different reference solutions.The authors thank the Ministerio de Ciencia y Tecnologia for the support received in the framework of the projects DPI2010-20990, DPI2010-20542 and to the Generalitat Valenciana, Programme PROMETEO 2012/023.Giner Maravilla, E.; Bognet, B.; Ródenas, J.; Leygue, A.; Fuenmayor Fernández, FJ.; Chinesta Soria, FJ. (2013). The Proper Generalized Decomposition (PGD) as a numerical procedure to solve 3D cracked plates in linear elastic fracture mechanics. International Journal of Solids and Structures. 50(10):1710-1720. https://doi.org/10.1016/j.ijsolstr.2013.01.039S17101720501

A Physically-Based Fractional Diffusion Model for Semi-Dilute Suspensions of Rods in a Newtonian Fluid

[EN] The rheological behaviour of suspensions involving interacting (functionalized) rods remains nowadays incompletely understood, in particular with regard to the evolution of the elastic modulus with the applied frequency in small-amplitude oscillatory flows. In a previous work, we addressed this issue by assuming a fractional diffusion mechanism, however the approach followed was purely phenomenological. The present work revisits the topic from a phys ical viewpoint, with the aim of justifying the fractional nature of diffusion. After accomplishing this first objective, we explore by means of numerical ex periments the consequences of the proposed fractional modelling approach in linear and non-linear rheology.Nadal, E.; Aguado-López, JV.; Abisset-Chavanne, E.; Chinesta Soria, FJ.; Keunings, R.; Cueto, E. (2017). A Physically-Based Fractional Diffusion Model for Semi-Dilute Suspensions of Rods in a Newtonian Fluid. Applied Mathematical Modelling. 51:58-67. https://doi.org/10.1016/j.apm.2017.06.009S58675

Describing and Modeling Rough Composites Surfaces by Using Topological Data Analysis and Fractional Brownian Motion

Many composite manufacturing processes employ the consolidation of pre-impregnated preforms. However, in order to obtain adequate performance of the formed part, intimate contact and molecular diffusion across the different composites’ preform layers must be ensured. The latter takes place as soon as the intimate contact occurs and the temperature remains high enough during the molecular reptation characteristic time. The former, in turn, depends on the applied compression force, the temperature and the composite rheology, which, during the processing, induce the flow of asperities, promoting the intimate contact. Thus, the initial roughness and its evolution during the process, become critical factors in the composite consolidation. Processing optimization and control are needed for an adequate model, enabling it to infer the consolidation degree from the material and process features. The parameters associated with the process are easily identifiable and measurable (e.g., temperature, compression force, process time, ⋯). The ones concerning the materials are also accessible; however, describing the surface roughness remains an issue. Usual statistical descriptors are too poor and, moreover, they are too far from the involved physics. The present paper focuses on the use of advanced descriptors out-performing usual statistical descriptors, in particular those based on the use of homology persistence (at the heart of the so-called topological data analysis—TDA), and their connection with fractional Brownian surfaces. The latter constitutes a performance surface generator able to represent the surface evolution all along the consolidation process, as the present paper emphasizes

Real time parameter identification and solution reconstruction from experimental data using the Proper Generalized Decomposition

Some industrial processes are modelled by parametric partial differential equations. Integrating computational modelling and data assimilation into the control process requires obtaining a solution of the numerical model at the characteristic frequency of the process (realtime). This paper introduces a computational strategy allowing to efficiently exploit measurements of those industrial processes, providing the solution of the model at the required frequency. This is particularly interesting in the framework of control algorithms that rely on a model involving a set of parameters. For instance, the curing process of a composite material is modelled as a thermo-mechanical problem whose corresponding parameters describe the thermal and mechanical behaviours. In this context, the information available (measurements) is used to update the parameters of the model and to produce new values of the control variables (data assimilation). The methodology presented here is devised to ensure the possibility of having a response in real-time of the problem and therefore the capability of integrating it in the control scheme. The Proper Generalized Decomposition is used to describe the solution in the multi-parametric space. The realtime data assimilation requires a further simplification of the solution representation that better fits the data (reconstructed solution) and it provides an implicit parameter identification. Moreover, the analysis of the assimilated data sensibility with respect to the points where the measurements are taken suggests a criterion to locate of the sensors.UPV's authors thank the financial support from Universitat Politecnica de Valencia and Generalitat Valenciana (PROMETEO/2012/023).Nadal Soriano, E.; Chinesta Soria, FJ.; Díez Mejia, P.; Fuenmayor Fernández, FJ.; Denia Guzmán, FD. (2015). Real time parameter identification and solution reconstruction from experimental data using the Proper Generalized Decomposition. Computer Methods in Applied Mechanics and Engineering. 296(1):113-128. doi:10.1016/j.cma.2015.07.020S113128296

Tensor representation of non-linear models using cross approximations

This is a post-peer-review, pre-copyedit version of an article published in Journal of scientific computing. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10915-019-00917-2Tensor representations allow compact storage and efficient manipulation of multi-dimensional data. Based on these, tensor methods build low-rank subspaces for the solution of multi-dimensional and multi-parametric models. However, tensor methods cannot always be implemented efficiently, specially when dealing with non-linear models. In this paper, we discuss the importance of achieving a tensor representation of the model itself for the efficiency of tensor-based algorithms. We investigate the adequacy of interpolation rather than projection-based approaches as a means to enforce such tensor representation, and propose the use of cross approximations for models in moderate dimension. Finally, linearization of tensor problems is analyzed and several strategies for the tensor subspace construction are proposed.Peer Reviewe