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We propose a novel approach for deformation-aware neural networks that learn the weighting and synthesis of dense volumetric deformation fields. Our method specifically targets the space-time representation of physical surfaces from liquid…
A slow decaying Kolmogorov n-width of the solution manifold of a parametric partial differential equation precludes the realization of efficient linear projection-based reduced-order models. This is due to the high dimensionality of the…
Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that…
Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…
Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of…
Efficient planning of assembly motions is a long standing challenge in the field of robotics that has been primarily tackled with reinforcement learning and sampling-based methods by using extensive physics simulations. This paper proposes…
The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover,…
Multivariate time series anomaly detection is a crucial problem in many industrial and research applications. Timely detection of anomalies allows, for instance, to prevent defects in manufacturing processes and failures in cyberphysical…
We implement stacked denoising autoencoders, a class of neural networks that are capable of learning powerful representations of high dimensional data. We describe stochastic gradient descent for unsupervised training of autoencoders, as…
Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…
Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may…
This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage…
The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…
Computing resonance and anti-resonance backbone curves in complex nonlinear mechanical systems is of high engineering relevance but remains computationally challenging, especially for large finite-element (FE) models. Existing…
A deep equilibrium model uses implicit layers, which are implicitly defined through an equilibrium point of an infinite sequence of computation. It avoids any explicit computation of the infinite sequence by finding an equilibrium point…
Simulation and optimization are crucial for advancing the engineering design of complex systems and processes. Traditional optimization methods require substantial computational time and effort due to their reliance on resource-intensive…
In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…
In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…
Artificial neural networks, widely recognised for their role in machine learning, are now transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems and enabling the…
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…