Related papers: Low-dimensional geometry learning for turbulence p…

Latent representations are an important theme in modern machine learning. Any network training with the notion of locality introduces a latent geometry which we can analyze with the help of differential geometry, specifically information…

We apply machine learning, a powerful method for uncovering complex correlations in high-dimensional data, to the galaxy-halo connection of cosmological hydrodynamical simulations. The mapping between galaxy and halo variables is stochastic…

In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…

Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy…

We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss…

Grokking -- the delayed transition from memorization to generalization in small algorithmic tasks -- remains poorly understood. We present a geometric analysis of optimization dynamics in transformers trained on modular arithmetic. PCA of…

The rapid expansion of mega-constellations in low Earth orbits has posed significant challenges to space traffic management, necessitating periodic inspections of satellites to ensure the sustainability of the space environment when…

Legged robot locomotion requires the planning of stable reference trajectories, especially while traversing uneven terrain. The proposed trajectory optimization framework is capable of generating dynamically stable base and footstep…

A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously…

Time-optimal trajectories drive quadrotors to their dynamic limits, but computing such trajectories involves solving non-convex problems via iterative nonlinear optimization, making them prohibitively costly for real-time applications. In…

We consider distributed optimization as motivated by machine learning in a multi-agent system: each agent holds local data and the goal is to minimize an aggregate loss function over a common model, via an interplay of local training and…

Although the basic concept of a stellarator was known since the early days of fusion research, advances in computational technology have enabled the modelling of increasingly complicated devices, leading up to the construction of…

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…

Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…

A novel approach to expedite design optimization of nonlinear beam dynamics in storage rings is proposed and demonstrated in this study. At each iteration, a neural network surrogate model is used to suggest new trial solutions in a…

Exploration systems are critical for enhancing the autonomy of robots. Due to the unpredictability of the future planning space, existing methods either adopt an inefficient greedy strategy or require a lot of resources to obtain a global…

We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…

In this paper we study the efficacy of combining machine-learning methods with projection-based model reduction techniques for creating data-driven surrogate models of computationally expensive, high-fidelity physics models. Such surrogate…

Through periodic Training we can gradually buildup a reproducible responses in a disordered system where plasticity dominates over elasticity as is known in classical amorphous materials and soft matter 1, 6. Here we show that a similar…

The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…