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Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…

We propose a differentiable optimization framework for flip-and-landing trajectory design of reusable spacecraft, exemplified by the Starship vehicle. A deep neural network surrogate, trained on high-fidelity CFD data, predicts aerodynamic…

In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Quadratic regularization penalizes transport couplings by the squared $L^2$…

Multidimensional magneto-hydrodynamical (MHD) simulations coupled with stochastic differential equations (SDEs) adapted to test particle acceleration and transport in complex astrophysical flows are presented. The numerical scheme allows…

Nuclear fusion plays a pivotal role in the quest for reliable and sustainable energy production. A major roadblock to achieving commercially viable fusion power is understanding plasma turbulence, which can significantly degrade plasma…

We present a quantum-assisted generative algorithm for synthetic tracks of Lagrangian tracer particles in a turbulent shear flow. The parallelism and sampling properties of quantum algorithms are used to build and optimize a parametric…

High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…

Polaron defects are ubiquitous in materials and play an important role in many processes involving carrier mobility, charge transfer and surface reactivity. Determining the spatial distribution of small polarons is essential to understand…

Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture…

Surrogate modeling of non-linear oscillator networks remains challenging due to discrepancies between simplified analytical models and real-world complexity. To bridge this gap, we investigate hybrid reservoir computing, combining reservoir…

We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces…

The dynamics of a turbulent flow tend to occupy only a portion of the phase space at a statistically stationary regime. From a dynamical systems point of view, this portion is the attractor. The knowledge of the turbulent attractor is…

Introducing genetic algorithms as a reliable and efficient tool to find ordered equilibrium structures, we predict minimum energy configurations of the square shoulder system for different values of corona width $\lambda$. Varying…

The learning rate schedule is one of the most impactful aspects of neural network optimization, yet most schedules either follow simple parametric functions or react only to short-term training signals. None of them are supported by a…

Transport in Hamiltonian systems with weak chaotic perturbations has been much studied in the past. In this paper, we introduce a new class of problems: transport in Hamiltonian systems with slowly changing phase space structure that are…

We present a framework for bi-level trajectory optimization in which a system's dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level…

Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…

Stochastic gradient descent (SGD) has been found to be surprisingly effective in training a variety of deep neural networks. However, there is still a lack of understanding on how and why SGD can train these complex networks towards a…