Predictions of complex flows remain a significant challenge for engineering systems. Computationally affordable predictions of turbulent flows generally require Reynolds-Averaged Navier–Stokes (RANS) simulations and Large-Eddy Simulation (LES), the predictive accuracy of which can be insufficient due to non-Boussinesq turbulence and/or unresolved multiphysics that preclude qualitative fidelity in certain regimes. For example, in turbulent combustion, flame–turbulence interactions can lead to inverse-cascade energy transfer, which violates the assumptions of many RANS and LES closures. We present an adjoint-based, solver-embedded data assimilation method to augment the RANS and LES equations using trusted data. This is accomplished using Python-native flow solvers that leverage differentiable programming techniques to construct the adjoint equations needed for optimization. We present applications to shock-tube ignition delay predictions, turbulent premixed jet flames, and shock-dominated nonequilibrium flows and discuss the potential of adjoint-based approaches for future machine learning applications.

In this talk, we will explore three flow configurations that illustrate the behaviour of slow-moving viscous fluids in confined geometries: viscous gravity currents, fracturing of shear-thinning fluids in a Hele-Shaw cell, and rectangular channel flows of non-Newtonian fluids. We will first develop simple mathematical models to describe each setup, and then we will compare the theoretical predictions from these models with laboratory experiments. As is often the case, we will see that even models that are grounded in solid physical principles often fail to accurately predict the real-world flow behaviour. Our aim is to identify the primary physical mechanisms absent from the model using laboratory experiments. We will then refine the mathematical models and see whether better agreement between theory and experiment can be achieved.

A fundamental question in neuroscience is to understand how information is represented in the activity of  tens of thousands of neurons in the brain. Towards this end, low-rank matrix and tensor decompositions are commonly used to identify correlates of behavior in high-dimensional neural data. In this talk I will first present a novel tensor decomposition based on the slice rank which is able to disentangle mixed modes of covarying patterns in data tensors. Second, to compliment this statistical approach, I will present our recent dynamical systems modelling of neural activity over learning. Rather than factorizing data tensors themselves, we instead fit a dynamical system to the data, while constraining the tensor of parameters to be low rank. Together these projects highlight how applications in neural data can inspire new classes of low-rank models.