3D semantic scene completion is critical for multiple downstream tasks in autonomous systems. It estimates missing geometric and semantic information in the acquired scene data. Due to the challenging real-world conditions, this task usually demands complex models that process multi-modal data to achieve acceptable performance. We propose a unique neural model, leveraging advances from the state space and diffusion generative modeling to achieve remarkable 3D semantic scene completion performance with monocular image input. Our technique processes the data in the conditioned latent space of a variational autoencoder where diffusion modeling is carried out with an innovative state space technique. A key component of our neural network is the proposed Skimba (Skip Mamba) denoiser, which is adept at efficiently processing long-sequence data. The Skimba diffusion model is integral to our 3D scene completion network, incorporating a triple Mamba structure, dimensional decomposition residuals and varying dilations along three directions. We also adopt a variant of this network for the subsequent semantic segmentation stage of our method. Extensive evaluation on the standard SemanticKITTI and SSCBench-KITTI360 datasets show that our approach not only outperforms other monocular techniques by a large margin, it also achieves competitive performance against stereo methods. The code is available at https://github.com/xrkong/skimba

Optical Character Recognition (OCR) is crucial to the National Library of Norway's (NLN) digitisation process as it converts scanned documents into machine-readable text. However, for the S\'ami documents in NLN's collection, the OCR accuracy is insufficient. Given that OCR quality affects downstream processes, evaluating and improving OCR for text written in S\'ami languages is necessary to make these resources accessible. To address this need, this work fine-tunes and evaluates three established OCR approaches, Transkribus, Tesseract and TrOCR, for transcribing S\'ami texts from NLN's collection. Our results show that Transkribus and TrOCR outperform Tesseract on this task, while Tesseract achieves superior performance on an out-of-domain dataset. Furthermore, we show that fine-tuning pre-trained models and supplementing manual annotations with machine annotations and synthetic text images can yield accurate OCR for S\'ami languages, even with a moderate amount of manually annotated data.

We focus on designing and solving the neutral inclusion problem via neural networks. The neutral inclusion problem has a long history in the theory of composite materials, and it is exceedingly challenging to identify the precise condition that precipitates a general-shaped inclusion into a neutral inclusion. Physics-informed neural networks (PINNs) have recently become a highly successful approach to addressing both forward and inverse problems associated with partial differential equations. We found that traditional PINNs perform inadequately when applied to the inverse problem of designing neutral inclusions with arbitrary shapes. In this study, we introduce a novel approach, Conformal mapping Coordinates Physics-Informed Neural Networks (CoCo-PINNs), which integrates complex analysis techniques into PINNs. This method exhibits strong performance in solving forward-inverse problems to construct neutral inclusions of arbitrary shapes in two dimensions, where the imperfect interface condition on the inclusion's boundary is modeled by training neural networks. Notably, we mathematically prove that training with a single linear field is sufficient to achieve neutrality for untrained linear fields in arbitrary directions, given a minor assumption. We demonstrate that CoCo-PINNs offer enhanced performances in terms of credibility, consistency, and stability.

Data assimilation (DA) is crucial for improving the accuracy of state estimation in complex dynamical systems by integrating observational data with physical models. Traditional solutions rely on either pure model-driven approaches, such as Bayesian filters that struggle with nonlinearity, or data-driven methods using deep learning priors, which often lack generalizability and physical interpretability. Recently, score-based DA methods have been introduced, focusing on learning prior distributions but neglecting explicit state transition dynamics, leading to limited accuracy improvements. To tackle the challenge, we introduce FlowDAS, a novel generative model-based framework using the stochastic interpolants to unify the learning of state transition dynamics and generative priors. FlowDAS achieves stable and observation-consistent inference by initializing from proximal previous states, mitigating the instability seen in score-based methods. Our extensive experiments demonstrate FlowDAS's superior performance on various benchmarks, from the Lorenz system to high-dimensional fluid super-resolution tasks. FlowDAS also demonstrates improved tracking accuracy on practical Particle Image Velocimetry (PIV) task, showcasing its effectiveness in complex flow field reconstruction.

We derive explicit equations governing the cumulative biases and weights in Deep Learning with ReLU activation function, based on gradient descent for the Euclidean cost in the input layer, and under the assumption that the weights are, in a precise sense, adapted to the coordinate system distinguished by the activations. We show that gradient descent corresponds to a dynamical process in the input layer, whereby clusters of data are progressively reduced in complexity ("truncated") at an exponential rate that increases with the number of data points that have already been truncated. We provide a detailed discussion of several types of solutions to the gradient flow equations. A main motivation for this work is to shed light on the interpretability question in supervised learning.

Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately remains challenging, often leading to soft enforcement that compromises convergence and reliability in complex domains. We propose a hybrid approach, PINN-FEM, which combines PINNs with finite element methods (FEM) to impose strong Dirichlet boundary conditions via domain decomposition. This method incorporates FEM-based representations near the boundary, ensuring exact enforcement without compromising convergence. Through six experiments of increasing complexity, PINN-FEM outperforms standard PINN models, showcasing superior accuracy and robustness. While distance functions and similar techniques have been proposed for boundary condition enforcement, they lack generality for real-world applications. PINN-FEM bridges this gap by leveraging FEM near boundaries, making it well-suited for industrial and scientific problems.

Distributed-memory implementations of numerical optimization algorithm, such as stochastic gradient descent (SGD), require interprocessor communication at every iteration of the algorithm. On modern distributed-memory clusters where communication is more expensive than computation, the scalability and performance of these algorithms are limited by communication cost. This work generalizes prior work on 1D $s$-step SGD and 1D Federated SGD with Averaging (FedAvg) to yield a 2D parallel SGD method (HybridSGD) which attains a continuous performance trade off between the two baseline algorithms. We present theoretical analysis which show the convergence, computation, communication, and memory trade offs between $s$-step SGD, FedAvg, 2D parallel SGD, and other parallel SGD variants. We implement all algorithms in C++ and MPI and evaluate their performance on a Cray EX supercomputing system. Our empirical results show that HybridSGD achieves better convergence than FedAvg at similar processor scales while attaining speedups of $5.3\times$ over $s$-step SGD and speedups up to $121\times$ over FedAvg when used to solve binary classification tasks using the convex, logistic regression model on datasets obtained from the LIBSVM repository.

Legged robots with advanced manipulation capabilities have the potential to significantly improve household duties and urban maintenance. Despite considerable progress in developing robust locomotion and precise manipulation methods, seamlessly integrating these into cohesive whole-body control for real-world applications remains challenging. In this paper, we present a modular framework for robust and generalizable whole-body loco-manipulation controller based on a single arm-mounted camera. By using reinforcement learning (RL), we enable a robust low-level policy for command execution over 5 dimensions (5D) and a grasp-aware high-level policy guided by a novel metric, Generalized Oriented Reachability Map (GORM). The proposed system achieves state-of-the-art one-time grasping accuracy of 89% in the real world, including challenging tasks such as grasping transparent objects. Through extensive simulations and real-world experiments, we demonstrate that our system can effectively manage a large workspace, from floor level to above body height, and perform diverse whole-body loco-manipulation tasks.

The energy transition necessitates new congestion management methods. One such method is controlling the grid topology with machine learning (ML). This approach has gained popularity following the Learning to Run a Power Network (L2RPN) competitions. Graph neural networks (GNNs) are a class of ML models that reflect graph structure in their computation, which makes them suitable for power grid modeling. Various GNN approaches for topology control have thus been proposed. We propose the first GNN model for grid topology control that uses only GNN layers. Additionally, we identify the busbar information asymmetry problem that the popular homogeneous graph representation suffers from, and propose a heterogeneous graph representation to resolve it. We train both homogeneous and heterogeneous GNNs and fully connected neural networks (FCNN) baselines on an imitation learning task. We evaluate the models according to their classification accuracy and grid operation ability. We find that the heterogeneous GNNs perform best on in-distribution networks, followed by the FCNNs, and lastly, the homogeneous GNNs. We also find that both GNN types generalize better to out-of-distribution networks than FCNNs.

Accurate prediction of electricity prices plays an essential role in the electricity market. To reflect the uncertainty of electricity prices, price intervals are predicted. This paper proposes a novel prediction interval construction method. A conditional generative adversarial network is first presented to generate electricity price scenarios, with which the prediction intervals can be constructed. Then, different generated scenarios are stacked to obtain the probability densities, which can be applied to accurately reflect the uncertainty of electricity prices. Furthermore, a reinforced prediction mechanism based on the volatility level of weather factors is introduced to address the spikes or volatile prices. A case study is conducted to verify the effectiveness of the proposed novel prediction interval construction method. The method can also provide the probability density of each price scenario within the prediction interval and has the superiority to address the volatile prices and price spikes with a reinforced prediction mechanism.