Additionally, we introduce a Bézier-boundary gradient approximation strategy within our framework to keep the "differentiability"

In this paper, we present DiffSketcher, an innovative algorithm that creates vectorized free-hand sketches using natural language input.

Let B be the maximum difference betweenU1t and U2t, and let (π,θ1,θ2) be a Nash Equilibrium forG. Let π1 be the best response to the first teacher (with utilityU1t) and let π1+2 be the best response policy to the joint teacher. This result shows that as we reduce the number of random episodes, the approximation to aminimax regret strategy improves. Let G be the dual curriculum game in which the first teacher maximizes regret, so U1t = URt, and the second teacher plays randomly, soU2t = UUt . Finally,we need to show thatπ2+3 isoptimal for the student.

To address this, we leverage parametric modular structure to learn component-level surrogates, enabling cheaper high-fidelity simulation. We use a neural network to model the stored potential energy in a component given boundary conditions.

Abstract-- Hard-constraint trajectory planners often rely on commercial solvers and demand substantial computational resources. Existing soft-constraint methods achieve faster computation, but either (1) decouple spatial and temporal optimization or (2) restrict the search space. T o overcome these limitations, we introduce MIGHTY, a Hermite spline-based planner that performs spatiotemporal optimization while fully leveraging the continuous search space of a spline. In simulation, MIGHTY achieves a 9.3% reduction in computation time and a 13.1% reduction in travel time over state-of-the-art baselines, with a 100% success rate. In hardware, MIGHTY completes multiple high-speed flights up to 6.7 m/s in a cluttered static environment and long-duration flights with dynamically added obstacles. Trajectory planning for autonomous navigation has been extensively studied, with a wide variety of parameterizations and formulations [3], [6], [7], [9], [12], [14]-[17], [19]-[23].

Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise sensitivity in complex mechanical systems. The Lagrangian formalism offers a promising alternative, as it typically avoids rational expressions and provides a more concise representation of system dynamics. However, existing Lagrangian identification methods are significantly affected by measurement noise and limited data availability. This paper presents a novel differentiable sparse identification framework that addresses these limitations through three key contributions: (1) the first integration of cubic B-Spline approximation into Lagrangian system identification, enabling accurate representation of complex nonlinearities, (2) a robust equation discovery mechanism that effectively utilizes measurements while incorporating known physical constraints, (3) a recursive derivative computation scheme based on B-spline basis functions, effectively constraining higher-order derivatives and reducing noise sensitivity on second-order dynamical systems. The proposed method demonstrates superior performance and enables more accurate and reliable extraction of physical laws from noisy data, particularly in complex mechanical systems compared to baseline methods.