MetaNO: How to Transfer Your Knowledge on Learning Hidden Physics

Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important impact on learning and predicting the response of a complex physical system directly from observational data. Since the data acquisition in this context is commonly challenging and costly, the call of utilization and transfer of existing knowledge to new and unseen physical systems is even more acute. Herein, we propose a novel meta-learning approach for neural operators, which can be seen as transferring the knowledge of solution operators between governing (unknown) PDEs with varying parameter fields. Our approach is a provably universal solution operator for multiple PDE solving tasks, with a key theoretical observation that underlying parameter fields can be captured in the first layer of neural operator models, in contrast to typical final-layer transfer in existing meta-learning methods. As applications, we demonstrate the efficacy of our proposed approach on PDE-based datasets and a real-world material modeling problem, illustrating that our method can handle complex and nonlinear physical response learning tasks while greatly improving the sampling efficiency in unseen tasks.

Knowledge-augmented Deep Learning and Its Applications: A Survey

Deep learning models, though having achieved great success in many different fields over the past years, are usually data hungry, fail to perform well on unseen samples, and lack of interpretability. Various prior knowledge often exists in the target domain and their use can alleviate the deficiencies with deep learning. To better mimic the behavior of human brains, different advanced methods have been proposed to identify domain knowledge and integrate it into deep models for data-efficient, generalizable, and interpretable deep learning, which we refer to as knowledge-augmented deep learning (KADL). In this survey, we define the concept of KADL, and introduce its three major tasks, i.e., knowledge identification, knowledge representation, and knowledge integration. Different from existing surveys that are focused on a specific type of knowledge, we provide a broad and complete taxonomy of domain knowledge and its representations. Based on our taxonomy, we provide a systematic review of existing techniques, different from existing works that survey integration approaches agnostic to taxonomy of knowledge. This survey subsumes existing works and offers a bird's-eye view of research in the general area of knowledge-augmented deep learning. The thorough and critical reviews of numerous papers help not only understand current progresses but also identify future directions for the research on knowledge-augmented deep learning.

Learning and Retrieval from Prior Data for Skill-based Imitation Learning

Imitation learning offers a promising path for robots to learn general-purpose behaviors, but traditionally has exhibited limited scalability due to high data supervision requirements and brittle generalization. Inspired by recent advances in multi-task imitation learning, we investigate the use of prior data from previous tasks to facilitate learning novel tasks in a robust, data-efficient manner. To make effective use of the prior data, the robot must internalize knowledge from past experiences and contextualize this knowledge in novel tasks. To that end, we develop a skill-based imitation learning framework that extracts temporally extended sensorimotor skills from prior data and subsequently learns a policy for the target task that invokes these learned skills. We identify several key design choices that significantly improve performance on novel tasks, namely representation learning objectives to enable more predictable skill representations and a retrieval-based data augmentation mechanism to increase the scope of supervision for policy training. On a collection of simulated and real-world manipulation domains, we demonstrate that our method significantly outperforms existing imitation learning and offline reinforcement learning approaches. Videos and code are available at https://ut-austin-rpl.github.io/sailor

Phasic Self-Imitative Reduction for Sparse-Reward Goal-Conditioned Reinforcement Learning

It has been a recent trend to leverage the power of supervised learning (SL) towards more effective reinforcement learning (RL) methods. We propose a novel phasic approach by alternating online RL and offline SL for tackling sparse-reward goal-conditioned problems. In the online phase, we perform RL training and collect rollout data while in the offline phase, we perform SL on those successful trajectories from the dataset. To further improve sample efficiency, we adopt additional techniques in the online phase including task reduction to generate more feasible trajectories and a value-difference-based intrinsic reward to alleviate the sparse-reward issue. We call this overall algorithm, PhAsic self-Imitative Reduction (PAIR). PAIR substantially outperforms both non-phasic RL and phasic SL baselines on sparse-reward goal-conditioned robotic control problems, including a challenging stacking task. PAIR is the first RL method that learns to stack 6 cubes with only 0/1 success rewards from scratch.

Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel nonlocal neural operator, which we refer to as nonlocal kernel network (NKN), that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images. Our NKN stems from the interpretation of the neural network as a discrete nonlocal diffusion reaction equation that, in the limit of infinite layers, is equivalent to a parabolic nonlocal equation, whose stability is analyzed via nonlocal vector calculus. The resemblance with integral forms of neural operators allows NKNs to capture long-range dependencies in the feature space, while the continuous treatment of node-to-node interactions makes NKNs resolution independent. The resemblance with neural ODEs, reinterpreted in a nonlocal sense, and the stable network dynamics between layers allow for generalization of NKN's optimal parameters from shallow to deep networks. This fact enables the use of shallow-to-deep initialization techniques. Our tests show that NKNs outperform baseline methods in both learning governing equations and image classification tasks and generalize well to different resolutions and depths.

Onsite Non-Line-of-Sight Imaging via Online Calibrations

There has been an increasing interest in deploying non-line-of-sight (NLOS) imaging systems for recovering objects behind an obstacle. Existing solutions generally pre-calibrate the system before scanning the hidden objects. Onsite adjustments of the occluder, object and scanning pattern require re-calibration. We present an online calibration technique that directly decouples the acquired transients at onsite scanning into the LOS and hidden components. We use the former to directly (re)calibrate the system upon changes of scene/obstacle configurations, scanning regions, and scanning patterns whereas the latter for hidden object recovery via spatial, frequency or learning based techniques. Our technique avoids using auxiliary calibration apparatus such as mirrors or checkerboards and supports both laboratory validations and real-world deployments.

Logical Credal Networks

This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional probability bounds of logic formulas, this logic specifies a set of probability distributions over all interpretations. On the one hand, our approach allows propositional and first-order logic formulas with few restrictions, e.g., without requiring acyclicity. On the other hand, it has a Markov condition similar to Bayesian networks and Markov random fields that is critical in real-world applications. Having both these properties makes this logic unique, and we investigate its performance on maximum a posteriori inference tasks, including solving Mastermind games with uncertainty and detecting credit card fraud. The results show that the proposed method outperforms existing approaches, and its advantage lies in aggregating multiple sources of imprecise information.

Image Feature Information Extraction for Interest Point Detection: A Comprehensive Review

Interest point detection is one of the most fundamental and critical problems in computer vision and image processing. In this paper, we carry out a comprehensive review on image feature information (IFI) extraction techniques for interest point detection. To systematically introduce how the existing interest point detection methods extract IFI from an input image, we propose a taxonomy of the IFI extraction techniques for interest point detection. According to this taxonomy, we discuss different types of IFI extraction techniques for interest point detection. Furthermore, we identify the main unresolved issues related to the existing IFI extraction techniques for interest point detection and any interest point detection methods that have not been discussed before. The existing popular datasets and evaluation standards are provided and the performances for eighteen state-of-the-art approaches are evaluated and discussed. Moreover, future research directions on IFI extraction techniques for interest point detection are elaborated.

DAGs with No Curl: An Efficient DAG Structure Learning Approach

Recently directed acyclic graph (DAG) structure learning is formulated as a constrained continuous optimization problem with continuous acyclicity constraints and was solved iteratively through subproblem optimization. To further improve efficiency, we propose a novel learning framework to model and learn the weighted adjacency matrices in the DAG space directly. Specifically, we first show that the set of weighted adjacency matrices of DAGs are equivalent to the set of weighted gradients of graph potential functions, and one may perform structure learning by searching in this equivalent set of DAGs. To instantiate this idea, we propose a new algorithm, DAG-NoCurl, which solves the optimization problem efficiently with a two-step procedure: 1) first we find an initial cyclic solution to the optimization problem, and 2) then we employ the Hodge decomposition of graphs and learn an acyclic graph by projecting the cyclic graph to the gradient of a potential function. Experimental studies on benchmark datasets demonstrate that our method provides comparable accuracy but better efficiency than baseline DAG structure learning methods on both linear and generalized structural equation models, often by more than one order of magnitude.