Related papers: Physics-Informed Neural Controlled Differential Eq…

In this paper we propose a new methodology for decision-making under uncertainty using recent advancements in the areas of nonlinear stochastic optimal control theory, applied mathematics, and machine learning. Grounded on the fundamental…

Annually, a large number of injuries and deaths around the world are related to motor vehicle accidents. This value has recently been reduced to some extent, via the use of driver-assistance systems. Developing driver-assistance systems…

Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this…

Imitation learning is an intuitive approach for teaching motion to robotic systems. Although previous studies have proposed various methods to model demonstrated movement primitives, one of the limitations of existing methods is that the…

Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…

The navigation of robots in dynamic urban environments, requires elaborated anticipative strategies for the robot to avoid collisions with dynamic objects, like bicycles or pedestrians, and to be human aware. We have developed and analyzed…

We consider the joint design and control of discrete-time stochastic dynamical systems over a finite time horizon. We formulate the problem as a multi-step optimization problem under uncertainty seeking to identify a system design and a…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed…

Pedestrian trajectory forecasting is a fundamental task in multiple utility areas, such as self-driving, autonomous robots, and surveillance systems. The future trajectory forecasting is multi-modal, influenced by physical interaction with…

Motion prediction of surrounding vehicles is one of the most important tasks handled by a self-driving vehicle, and represents a critical step in the autonomous system necessary to ensure safety for all the involved traffic actors. Recently…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs). However, their generalization capabilities across varying scenarios remain limited. To…

We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…

Mental simulation is a critical cognitive function for goal-directed behavior because it is essential for assessing actions and their consequences. When a self-generated or externally specified goal is given, a sequence of actions that is…

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle,…

Millirobots are a promising robotic platform for many applications due to their small size and low manufacturing costs. Legged millirobots, in particular, can provide increased mobility in complex environments and improved scaling of…

The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…

In this paper we investigate infinite horizon optimal control problems for parametrized partial differential equations. We are interested in feedback control via dynamic programming equations which is well-known to suffer from the curse of…

Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…

Safe operation of systems such as robots requires them to plan and execute trajectories subject to safety constraints. When those systems are subject to uncertainties in their dynamics, it is challenging to ensure that the constraints are…