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Many important multi-component crystalline solids undergo mechanochemical spinodal decomposition: a phase transformation in which the compositional redistribution is coupled with structural changes of the crystal, resulting in dynamically…

Constitutive modelling is crucial for engineering design and simulations to accurately describe material behavior. However, traditional phenomenological models often struggle to capture the complexities of real materials under varying…

It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with…

A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…

Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…

Physics-inspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases. These models, however, are challenging to apply to many real world…

We model acoustic dynamics in space and time from synthetic sensor data. The tasks are (i) to predict and extrapolate the spatiotemporal dynamics, and (ii) reconstruct the acoustic state from partial observations. To achieve this, we…

The weights of neural networks (NNs) have recently gained prominence as a new data modality in machine learning, with applications ranging from accuracy and hyperparameter prediction to representation learning or weight generation. One…

Recent work suggests that changing Convolutional Neural Network (CNN) architecture by introducing a bottleneck in the second layer can yield changes in learned function. To understand this relationship fully requires a way of quantitatively…

Nested Effects Models (NEMs) are a class of graphical models introduced to analyze the results of gene perturbation screens. NEMs explore noisy subset relations between the high-dimensional outputs of phenotyping studies, e.g. the effects…

Emulator embedded neural networks, which are a type of physics informed neural network, leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. Multiple realizations of the neural network…

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…

Despite the remarkable success of large large-scale neural networks, we still lack unified notation for thinking about and describing their representational spaces. We lack methods to reliably describe how their representations are…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use…

Anisotropic material properties, such as the thermal conductivities of engineering composites, exhibit variability due to inherent material heterogeneity and manufacturing-related uncertainties. Mathematically, these properties are modeled…

Current neural network (NN) models can learn patterns from data points with historical dependence. Specifically, in natural language processing (NLP), sequential learning has transitioned from recurrence-based architectures to…

Injecting structure into neural networks enables learning functions that satisfy invariances with respect to subsets of inputs. For instance, when learning generative models using neural networks, it is advantageous to encode the…