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Microstructural evolution is a key aspect of understanding and exploiting the structure-property-performance relation of materials. Modeling microstructure evolution usually relies on coarse-grained simulations with evolution principles…
Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further this understanding by developing statistical guarantees for…
Forecasting the evolution of contagion dynamics is still an open problem to which mechanistic models only offer a partial answer. To remain mathematically or computationally tractable, these models must rely on simplifying assumptions,…
We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent…
Robustness of convolutional neural networks (CNNs) has gained in importance on account of adversarial examples, i.e., inputs added as well-designed perturbations that are imperceptible to humans but can cause the model to predict…
Advancements in deep learning and machine learning have improved the ability to model complex, nonlinear relationships, such as those encountered in complex material inverse problems. However, the effectiveness of these methods often…
The present paradigm in design and modelling of lattice architected mechanical metamaterials is mostly limited to traditional numerical methods like finite element analysis. Recently, the use of machine learning and artificial intelligence…
In deep learning, neural networks serve as noisy channels between input data and its representation. This perspective naturally relates deep learning with the pursuit of constructing channels with optimal performance in information…
To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…
In the design of tensegrity structures, traditional form-finding methods utilize kinematic and static approaches to identify geometric configurations that achieve equilibrium. However, these methods often fall short when applied to actual…
Context: Automated software defect prediction (SDP) methods are increasingly applied, often with the use of machine learning (ML) techniques. Yet, the existing ML-based approaches require manually extracted features, which are cumbersome,…
Unsupervised structure learning in high-dimensional time series data has attracted a lot of research interests. For example, segmenting and labelling high dimensional time series can be helpful in behavior understanding and medical…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
We present a data-driven method for learning to generate animations of 3D garments using a 2D image diffusion model. In contrast to existing methods, typically based on fully connected networks, graph neural networks, or generative…
Using established principles from Statistics and Information Theory, we show that invariance to nuisance factors in a deep neural network is equivalent to information minimality of the learned representation, and that stacking layers and…
In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…
Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws. Recent developments in neural networks have enabled the…
Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension…
The ability to predict future states of the environment is a central pillar of intelligence. At its core, effective prediction requires an internal model of the world and an understanding of the rules by which the world changes. Here, we…
Magnetic materials host a wealth of nonlinear dynamics, textures, and topological defects. This is possible due to the competition between strong nonlinearity and dispersion that act at the atomic scale as well as long-range interactions.…