Related papers: SaddleScape V1.0: A Python Package for Constructin…

Constructing HD semantic maps is a central component of autonomous driving. However, traditional pipelines require a vast amount of human efforts and resources in annotating and maintaining the semantics in the map, which limits its…

The proliferation of saddle points, rather than poor local minima, is increasingly understood to be a primary obstacle in large-scale non-convex optimization for machine learning. Variable elimination algorithms, like Variable Projection…

We have developed an open-source software package (SedSimple) for stratigraphic forward modeling. It is aimed for use in research and education. The package uses ASCII files for input and output to facilitate understanding, debugging and…

We present a class of simple algorithms that allows to find the reaction path in systems with a complex potential energy landscape. The approach does not need any knowledge on the product state and does not require the calculation of any…

We present WayveScenes101, a dataset designed to help the community advance the state of the art in novel view synthesis that focuses on challenging driving scenes containing many dynamic and deformable elements with changing geometry and…

The convergence behaviour of first-order methods can be severely slowed down when applied to high-dimensional non-convex functions due to the presence of saddle points. If, additionally, the saddles are surrounded by large plateaus, it is…

This monograph presents the design, implementation, and evaluation of Pyroclast, a modular high-performance Python framework for large-scale geodynamic simulations. Pyroclast addresses limitations of legacy geodynamics solvers, often…

Hybrid modelling enhances the accuracy and predictive capability of dynamic models by integrating first principles with data-driven methods, effectively mitigating epistemic uncertainties inherent in mechanistic approaches. However, hybrid…

We develop and analyze numerical discretization to the constrained high-index saddle dynamics, the dynamics searching for the high-index saddle points confined on the high-dimensional unit sphere. Compared with the saddle dynamics without…

We prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics, which serves as a powerful instrument in finding saddle points and constructing the solution landscapes of constrained systems…

A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from…

This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…

Achieving fully autonomous driving systems requires learning rational decisions in a wide span of scenarios, including safety-critical and out-of-distribution ones. However, such cases are underrepresented in real-world corpus collected by…

High definition (HD) maps have demonstrated their essential roles in enabling full autonomy, especially in complex urban scenarios. As a crucial layer of the HD map, lane-level maps are particularly useful: they contain geometrical and…

Accurate localization is essential for autonomous driving, but GNSS-based methods struggle in challenging environments such as urban canyons. Cross-view pose optimization offers an effective solution by directly estimating vehicle pose…

Camera-based 3D semantic scene completion (SSC) plays a crucial role in autonomous driving, enabling voxelized 3D scene understanding for effective scene perception and decision-making. Existing SSC methods have shown efficacy in improving…

In this work, we introduce SPADE, a path planning framework designed for autonomous navigation in dynamic environments using 3D scene graphs. SPADE combines hierarchical path planning with local geometric awareness to enable collision-free…

For a real valued function, a point is critical if its derivatives are zero, and a critical point is a saddle point if it is not a local extrema. In this paper, we study algorithms to find saddle points of general Morse index. Our approach…

Here we present a multiscale method to calculate the saddle point associated with the effective dynamics arising from a stochastic system which couples slow deterministic drift and fast stochastic dynamics. This problem is motivated by the…

Surface water dynamics play a critical role in Earth's climate system, influencing ecosystems, agriculture, disaster resilience, and sustainable development. Yet monitoring rivers and surface water at fine spatial and temporal scales…