Implicit representations such as Neural Radiance Fields (NeRF) have been shown to be very effective at novel view synthesis. However, these models typically require manual and careful human data collection for training. In this paper, we present AutoNeRF, a method to collect data required to train NeRFs using autonomous embodied agents. Our method allows an agent to explore an unseen environment efficiently and use the experience to build an implicit map representation autonomously. We compare the impact of different exploration strategies including handcrafted frontier-based exploration, end-to-end and modular approaches composed of trained high-level planners and classical low-level path followers. We train these models with different reward functions tailored to this problem and evaluate the quality of the learned representations on four different downstream tasks: classical viewpoint rendering, map reconstruction, planning, and pose refinement. Empirical results show that NeRFs can be trained on actively collected data using just a single episode of experience in an unseen environment, and can be used for several downstream robotic tasks, and that modular trained exploration models outperform other classical and end-to-end baselines. Finally, we show that AutoNeRF can reconstruct large-scale scenes, and is thus a useful tool to perform scene-specific adaptation as the produced 3D environment models can be loaded into a simulator to fine-tune a policy of interest.

One of the most exciting applications of artificial intelligence (AI) is automated scientific discovery based on previously amassed data, coupled with restrictions provided by known physical principles, including symmetries and conservation laws. Such automated hypothesis creation and verification can assist scientists in studying complex phenomena, where traditional physical intuition may fail. Here we develop a platform based on a generalized Onsager principle to learn macroscopic dynamical descriptions of arbitrary stochastic dissipative systems directly from observations of their microscopic trajectories. Our method simultaneously constructs reduced thermodynamic coordinates and interprets the dynamics on these coordinates. We demonstrate its effectiveness by studying theoretically and validating experimentally the stretching of long polymer chains in an externally applied field. Specifically, we learn three interpretable thermodynamic coordinates and build a dynamical landscape of polymer stretching, including the identification of stable and transition states and the control of the stretching rate. Our general methodology can be used to address a wide range of scientific and technological applications.

Although the applications of artificial intelligence especially deep learning had greatly improved various aspects of intelligent manufacturing, they still face challenges for wide employment due to the poor generalization ability, difficulties to establish high-quality training datasets, and unsatisfactory performance of deep learning methods. The emergence of large scale foundational models(LSFMs) had triggered a wave in the field of artificial intelligence, shifting deep learning models from single-task, single-modal, limited data patterns to a paradigm encompassing diverse tasks, multimodal, and pre-training on massive datasets. Although LSFMs had demonstrated powerful generalization capabilities, automatic high-quality training dataset generation and superior performance across various domains, applications of LSFMs on intelligent manufacturing were still in their nascent stage. A systematic overview of this topic was lacking, especially regarding which challenges of deep learning can be addressed by LSFMs and how these challenges can be systematically tackled. To fill this gap, this paper systematically expounded current statue of LSFMs and their advantages in the context of intelligent manufacturing. and compared comprehensively with the challenges faced by current deep learning models in various intelligent manufacturing applications. We also outlined the roadmaps for utilizing LSFMs to address these challenges. Finally, case studies of applications of LSFMs in real-world intelligent manufacturing scenarios were presented to illustrate how LSFMs could help industries, improve their efficiency.

It is challenging to model and control a tail-sitter unmanned aerial vehicle (UAV) because its blended wing body generates complicated nonlinear aerodynamic effects, such as wing lift, fuselage drag, and propeller-wing interactions. We therefore devised a hybrid aerodynamic modeling method and model predictive control (MPC) design for a quadrotor tail-sitter UAV. The hybrid model consists of the Newton-Euler equation, which describes quadrotor dynamics, and a feedforward neural network, which learns residual aerodynamic effects. This hybrid model exhibits high predictive accuracy at a low computational cost and was used to implement hybrid MPC, which optimizes the throttle, pitch angle, and roll angle for position tracking. The controller performance was validated in real-world experiments, which obtained a 57% tracking error reduction compared with conventional nonlinear MPC. External wind disturbance was also introduced and the experimental results confirmed the robustness of the controller to these conditions.

We introduce Neural Flow Maps, a novel simulation method bridging the emerging paradigm of implicit neural representations with fluid simulation based on the theory of flow maps, to achieve state-of-the-art simulation of inviscid fluid phenomena. We devise a novel hybrid neural field representation, Spatially Sparse Neural Fields (SSNF), which fuses small neural networks with a pyramid of overlapping, multi-resolution, and spatially sparse grids, to compactly represent long-term spatiotemporal velocity fields at high accuracy. With this neural velocity buffer in hand, we compute long-term, bidirectional flow maps and their Jacobians in a mechanistically symmetric manner, to facilitate drastic accuracy improvement over existing solutions. These long-range, bidirectional flow maps enable high advection accuracy with low dissipation, which in turn facilitates high-fidelity incompressible flow simulations that manifest intricate vortical structures. We demonstrate the efficacy of our neural fluid simulation in a variety of challenging simulation scenarios, including leapfrogging vortices, colliding vortices, vortex reconnections, as well as vortex generation from moving obstacles and density differences. Our examples show increased performance over existing methods in terms of energy conservation, visual complexity, adherence to experimental observations, and preservation of detailed vortical structures.

Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable to operator learning, discuss various neural network architectures, and explain how to employ numerical PDE solvers effectively. We also give advice on how to create and manage training data and conduct optimization. We offer intuition behind the various neural network architectures employed in operator learning by motivating them from the point-of-view of numerical linear algebra.

Many of the most fundamental laws of nature can be formulated as partial differential equations (PDEs). Understanding these equations is, therefore, of exceptional importance for many branches of modern science and engineering. However, since the general solution of many PDEs is unknown, the efficient approximate solution of these equations is one of humanity's greatest challenges. While multigrid represents one of the most effective methods for solving PDEs numerically, in many cases, the design of an efficient or at least working multigrid solver is an open problem. This thesis demonstrates that grammar-guided genetic programming, an evolutionary program synthesis technique, can discover multigrid methods of unprecedented structure that achieve a high degree of efficiency and generalization. For this purpose, we develop a novel context-free grammar that enables the automated generation of multigrid methods in a symbolically-manipulable formal language, based on which we can apply the same multigrid-based solver to problems of different sizes without having to adapt its internal structure. Treating the automated design of an efficient multigrid method as a program synthesis task allows us to find novel sequences of multigrid operations, including the combination of different smoothing and coarse-grid correction steps on each level of the discretization hierarchy. To prove the feasibility of this approach, we present its implementation in the form of the Python framework EvoStencils, which is freely available as open-source software. This implementation comprises all steps from representing the algorithmic sequence of a multigrid method in the form of a directed acyclic graph of Python objects to its automatic generation and optimization using the capabilities of the code generation framework ExaStencils and the evolutionary computation library DEAP.

The partially observable constrained optimization problems (POCOPs) impede data-driven optimization techniques since an infeasible solution of POCOPs can provide little information about the objective as well as the constraints. We endeavor to design an efficient and provable method for expensive POCOPs under the framework of constrained Bayesian optimization. Our method consists of two key components. Firstly, we present an improved design of the acquisition functions that introduces balanced exploration during optimization. We rigorously study the convergence properties of this design to demonstrate its effectiveness. Secondly, we propose a Gaussian process embedding different likelihoods as the surrogate model for a partially observable constraint. This model leads to a more accurate representation of the feasible regions compared to traditional classification-based models. Our proposed method is empirically studied on both synthetic and real-world problems. The results demonstrate the competitiveness of our method for solving POCOPs.

Error bounds are derived for sampling and estimation using a discretization of an intrinsically defined Langevin diffusion with invariant measure $d\mu_\phi \propto e^{-\phi} \mathrm{dvol}_g $ on a compact Riemannian manifold. Two estimators of linear functionals of $\mu_\phi $ based on the discretized Markov process are considered: a time-averaging estimator based on a single trajectory and an ensemble-averaging estimator based on multiple independent trajectories. Imposing no restrictions beyond a nominal level of smoothness on $\phi$, first-order error bounds, in discretization step size, on the bias and variances of both estimators are derived. The order of error matches the optimal rate in Euclidean and flat spaces, and leads to a first-order bound on distance between the invariant measure $\mu_\phi$ and a stationary measure of the discretized Markov process. Generality of the proof techniques, which exploit links between two partial differential equations and the semigroup of operators corresponding to the Langevin diffusion, renders them amenable for the study of a more general class of sampling algorithms related to the Langevin diffusion. Conditions for extending analysis to the case of non-compact manifolds are discussed. Numerical illustrations with distributions, log-concave and otherwise, on the manifolds of positive and negative curvature elucidate on the derived bounds and demonstrate practical utility of the sampling algorithm.

We propose an adaptive model-predictive controller that balances driving the system to a goal state and seeking system observations that are informative with respect to the parameters of a nonlinear autoregressive exogenous model. The controller's objective function is derived from an expected free energy functional and contains information-theoretic terms expressing uncertainty over model parameters and output predictions. Experiments illustrate how parameter uncertainty affects the control objective and evaluate the proposed controller for a pendulum swing-up task.