Related papers: Generalizable Motion Planning via Operator Learnin…
Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of…
This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…
Neural operators generalize neural networks to learn mappings between function spaces from data. They are commonly used to learn solution operators of parametric partial differential equations (PDEs) or propagators of time-dependent PDEs.…
Computationally efficient surrogates for parametrized physical models play a crucial role in science and engineering. Operator learning provides data-driven surrogates that map between function spaces. However, instead of full-field…
We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The objective function is traditionally defined by…
The current paradigm for motion planning generates solutions from scratch for every new problem, which consumes significant amounts of time and computational resources. For complex, cluttered scenes, motion planning approaches can often…
To enable safe and efficient human-robot collaboration in shared workspaces it is important for the robot to predict how a human will move when performing a task. While predicting human motion for tasks not known a priori is very…
We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and…
Training large neural networks (NNs) requires optimizing high-dimensional data-dependent loss functions. The optimization landscape of these functions is often highly complex and textured, even fractal-like, with many spurious local minima,…
Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original…
The success of building a high-resolution velocity model using machine learning is hampered by generalization limitations that often limit the success of the approach on field data. This is especially true when relying on neural operators…
Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network…
Learning-based methods have shown promising performance for accelerating motion planning, but mostly in the setting of static environments. For the more challenging problem of planning in dynamic environments, such as multi-arm assembly…
Planning collision-free motions for robots with many degrees of freedom is challenging in environments with complex obstacle geometries. Recent work introduced the idea of speeding up the planning by encoding prior experience of successful…
Neural network (NN)-based methods have emerged as an attractive approach for robot motion planning due to strong learning capabilities of NN models and their inherently high parallelism. Despite the current development in this direction,…
Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…
For partial differential equations on domains of arbitrary shapes, existing works of neural operators attempt to learn a mapping from geometries to solutions. It often requires a large dataset of geometry-solution pairs in order to obtain a…
General-sum differential games can approximate values solved by Hamilton-Jacobi-Isaacs (HJI) equations for efficient inference when information is incomplete. However, solving such games through conventional methods encounters the curse of…
Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…
We present a motion planning algorithm to compute collision-free and smooth trajectories for high-DOF robots interacting with humans in a shared workspace. Our approach uses offline learning of human actions along with temporal coherence to…