Markov Logic Networks are highly expressive statistical relational models that combine complex relational information expressed by the first-order logic formulas with the uncertainty represented by the use of the undirected probabilistic graphical models (Markov networks). They allow for representation of a relational structure and uncertainty in a very compact manner, leading to human-interpretable models. In this talk we will discuss the theoretical background of the Markov logic networks and showcase the application in the spoken language understanding domain.
Chemical vapour deposition (CVD) processes are famous for their complexity. That becomes evident when all the transport mechanisms and chemical reactions that take place inside a CVD reactor are considered. The implementation of a Computational Fluid Dynamics (CFD) model for the simulation of such processes is possible, however, the aforementioned complexity usually leads to high computational costs. For this reason, a purely data-driven approach is investigated. Several supervised learning algorithms are tested and their performance on the dataset is compared. This approach allows for efficient and accurate predictions, for entire reactor geometries and different set-ups at a fraction of the time that even a simplified CFD model would require.
Compared to conventional projection-based model-order-reduction, its neural-network acceleration has the advantage that the online simulations are equation-free, meaning that no system of equations needs to be solved iteratively. Consequently, no stiffness matrix needs to be constructed and the stress update needs to be computed only once per increment. In this talk, I will present a recurrent neural network, that we developed to accelerate a projection-based model-order-reduction of the elastoplastic mechanical behavior of an RVE. The resulting speedup is substantial, whilst all microstructural information is preserved.
Conventional finite element solvers are computationally expensive to solve non-linear partial differential equations, particularly they perform poorly in real time scale applications. In this work we propose a deep learning surrogate model which predicts nonlinear displacement solutions for hyper-elastic constitutive models in real time. We implement the Bayesian inference approach, thereby giving probabilistic predictions of displacement fields, capable of giving uncertainty of predictions. We implement our framework to benchmark hyper-elastic simulations to prove that it is extremely fast yet accurate.
The property of conformal predictors to guarantee the required accuracy rate, for example, 95%, makes this framework attractive in various practical applications. This property is achieved at a price of reduction in precision. In the case of conformal classification, the systems can output multiple class labels instead of one, in the case of classification – a numerical interval instead of one value. In this talk, we’ll discuss the theory behind conformal prediction and how the choice of a nonconformity function can influence the efficiency (how small the prediction set is) of the resulting classifier.
In the last decades, artificial neural networks (ANNs) have drawn academy and industry attention for their ability to represent and solve complex problems. ANNs use algorithms based on stochastic gradient descent (SGD) to learn data patterns from training examples, which tends to be time-consuming. Researchers are studying how to distribute this computation across multiple GPUs to reduce training time. Modern implementations rely on synchronously scaling up resources or asynchronously scaling them out using a centralized communication network. However, both of these approaches have communication bottlenecks, which may impair their scaling time. In this research, we create TensAIR, a framework that scales out the training of sparse ANNs models in an asynchronously and decentralized manner. Due to the commutative properties of SGD updates, we linearly scaled out the number of gradients computed per second with minimal impairment on the convergence of the models – relative to the models’ sparseness. These results indicate that TensAIR enables the training of sparse neural networks in significantly less time. We conjecture that this article may inspire further studies on the usage of sparse ANNs on time-sensitive scenarios like online machine learning, which until now would not be considered feasible.
Second-order methods techniques are widely used in the field of optimization and have been recently applied to neural networks with impressive results. In this seminar, I will present two applications of second-order methods for deep learning.
Delays in freight rail intermodal operations generate negative impacts on the railway industry, so identifying the causes associated to these delays is vital to mitigate operational risks. In this seminar, we will present a set of Machine Learning models that were trained to predict the delays in freight rail intermodal operations, and then the most suitable model was used to explore the significant predictors which cause those delays, using data from the National Railway Company of Luxembourg that connects Bettembourg with several EU countries.
Fracture across space and time: a journey through multiscale methods, model order reduction and machine learning
We review and connect in this paper two approaches to solve multi-scale fracture problems. Machine learning and model order reduction on the one hand and multi-scale methods on the other hand.
We explain as didactically as possible how material complexity has led to the need for acceleration methods and discuss advances in model selection and error estimation for such problems.
We show how model reduction/machine learning and standard multiscale methods both fails when dealing with localization problems occurring in fracture mechanics.
We conclude by discussing the possibility of digital twins and make a parallel with medical simulation.
A computational library for multiscale modeling of material failure H Talebi, M Silani, SPA Bordas, P Kerfriden, T Rabczuk Computational Mechanics 53 (5), 1047-1071
Bridging proper orthogonal decomposition methods and augmented Newton–Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems P Kerfriden, P Gosselet, S Adhikari, SPA Bordas Computer Methods in Applied Mechanics and Engineering 200 (5-8), 850-866
A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics P Kerfriden, O Goury, T Rabczuk, SPA Bordas Computer Methods in Applied Mechanics and Engineering 256, 169-188
Local/global model order reduction strategy for the simulation of quasi-brittle fracture P Kerfriden, JC Passieux, SPA Bordas International Journal for Numerical Methods in Engineering 89 (2), 154-179
Molecular Dynamics/XFEM Coupling by a Three Dimensional Extended Bridging Domain with Applications to Dynamic Brittle Fracture H Talebi, M Silani, S Bordas, P Kerfriden, T Rabczuk International Journal for Multiscale Computational Engineering 11 (6), 527-541
Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization O Goury, D Amsallem, SPA Bordas, WK Liu, P Kerfriden Computational Mechanics 58 (2), 213–234
Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation LAA Beex, P Kerfriden, T Rabczuk, SPA Bordas Computer Methods in Applied Mechanics and Engineering 279, 348–378
Statistical extraction of process zones and representative subspaces in fracture of random composite P Kerfriden, KM Schmidt, T Rabczuk, SPA Bordas International Journal for Multiscale Computational Engineering 11 (3), 253-287
Guaranteed error bounds in homogenisation: an optimum stochastic approach to preserve the numerical separation of scales D Alves Paladim, JP Moitinho de Almeida, SPA Bordas, P Kerfriden International Journal for Numerical Methods in Engineering 110 (2), 103–132
What makes data science different? A discussion involving statistics2. 0 and computational sciences C Ley, SPA Bordas International Journal of Data Science and Analytics 6 (3), 167-175
Mathematical modelling and artificial intelligence in Luxembourg: Twenty PhD students to be trained in data-driven modelling S Bordas, S Natarajan, A Zilian ERCIM News 115, 39-40
Second-order optimization techniques have been proven successful, but cannot be fully leveraged for neural networks due to infeasibility of hessian calculations. I will discuss an approximated way of computing the hessian for neural networks, which emerges from a careful analysis of the hessian chain rule and activation functions.
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