Model Predictive Control (MPC) is a state-of-the-art (SOTA) control technique which requires solving hard constrained optimization problems iteratively. For uncertain dynamics, analytical model based robust MPC imposes additional constraints, increasing the hardness of the problem. The problem exacerbates in performance-critical applications, when more compute is required in lesser time. Data-driven regression methods such as Neural Networks have been proposed in the past to approximate system dynamics. However, such models rely on high volumes of labeled data, in the absence of symbolic analytical priors. This incurs non-trivial training overheads. Physics-informed Neural Networks (PINNs) have gained traction for approximating non-linear system of ordinary differential equations (ODEs), with reasonable accuracy. In this work, we propose a Robust Adaptive MPC framework via PINNs (RAMP-Net), which uses a neural network trained partly from simple ODEs and partly from data. A physics loss is used to learn simple ODEs representing ideal dynamics. Having access to analytical functions inside the loss function acts as a regularizer, enforcing robust behavior for parametric uncertainties. On the other hand, a regular data loss is used for adapting to residual disturbances (non-parametric uncertainties), unaccounted during mathematical modelling. Experiments are performed in a simulated environment for trajectory tracking of a quadrotor. We report 7.8% to 43.2% and 8.04% to 61.5% reduction in tracking errors for speeds ranging from 0.5 to 1.75 m/s compared to two SOTA regression based MPC methods.
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Oblivious inference is the task of outsourcing a ML model, like neural-networks, without disclosing critical and sensitive information, like the model's parameters. One of the most prominent solutions for secure oblivious inference is based on a powerful cryptographic tools, like Homomorphic Encryption (HE) and/or multi-party computation (MPC). Even though the implementation of oblivious inference systems schemes has impressively improved the last decade, there are still significant limitations on the ML models that they can practically implement. Especially when both the ML model and the input data's confidentiality must be protected. In this paper, we introduce the notion of partially oblivious inference. We empirically show that for neural network models, like CNNs, some information leakage can be acceptable. We therefore propose a novel trade-off between security and efficiency. In our research, we investigate the impact on security and inference runtime performance from the CNN model's weights partial leakage. We experimentally demonstrate that in a CIFAR-10 network we can leak up to $80\%$ of the model's weights with practically no security impact, while the necessary HE-mutliplications are performed four times faster.
The use of mutual information as a tool in private data sharing has remained an open challenge due to the difficulty of its estimation in practice. In this paper, we propose InfoShape, a task-based encoder that aims to remove unnecessary sensitive information from training data while maintaining enough relevant information for a particular ML training task. We achieve this goal by utilizing mutual information estimators that are based on neural networks, in order to measure two performance metrics, privacy and utility. Using these together in a Lagrangian optimization, we train a separate neural network as a lossy encoder. We empirically show that InfoShape is capable of shaping the encoded samples to be informative for a specific downstream task while eliminating unnecessary sensitive information. Moreover, we demonstrate that the classification accuracy of downstream models has a meaningful connection with our utility and privacy measures.
Uncertainty quantification is crucial for assessing the predictive ability of AI algorithms. A large body of work (including normalizing flows and Bayesian neural networks) has been devoted to describing the entire predictive distribution (PD) of a target variable Y given input features $\mathbf{X}$. However, off-the-shelf PDs are usually far from being conditionally calibrated; i.e., the probability of occurrence of an event given input $\mathbf{X}$ can be significantly different from the predicted probability. Most current research on predictive inference (such as conformal prediction) concerns constructing calibrated prediction sets only. It is often believed that the problem of obtaining and assessing entire conditionally calibrated PDs is too challenging. In this work, we show that recalibration, as well as diagnostics of entire PDs, are indeed attainable goals in practice. Our proposed method relies on the idea of regressing probability integral transform (PIT) scores against $\mathbf{X}$. This regression gives full diagnostics of conditional coverage across the entire feature space and can be used to recalibrate misspecified PDs. We benchmark our corrected prediction bands against oracle bands and state-of-the-art predictive inference algorithms for synthetic data, including settings with a distributional shift. Finally, we produce calibrated PDs for two applications: (i) probabilistic nowcasting based on sequences of satellite images, and (ii) estimation of galaxy distances based on imaging data (photometric redshifts).
There has been an increasing interest in integrating physics knowledge and machine learning for modeling dynamical systems. However, very limited studies have been conducted on seismic wave modeling tasks. A critical challenge is that these geophysical problems are typically defined in large domains (i.e., semi-infinite), which leads to high computational cost. In this paper, we present a novel physics-informed neural network (PINN) model for seismic wave modeling in semi-infinite domain without the nedd of labeled data. In specific, the absorbing boundary condition is introduced into the network as a soft regularizer for handling truncated boundaries. In terms of computational efficiency, we consider a sequential training strategy via temporal domain decomposition to improve the scalability of the network and solution accuracy. Moreover, we design a novel surrogate modeling strategy for parametric loading, which estimates the wave propagation in semin-infinite domain given the seismic loading at different locations. Various numerical experiments have been implemented to evaluate the performance of the proposed PINN model in the context of forward modeling of seismic wave propagation. In particular, we define diverse material distributions to test the versatility of this approach. The results demonstrate excellent solution accuracy under distinctive scenarios.
Physics-Informed Neural Networks (PINNs) have become a kind of attractive machine learning method for obtaining solutions of partial differential equations (PDEs). Training PINNs can be seen as a semi-supervised learning task, in which only exact values of initial and boundary points can be obtained in solving forward problems, and in the whole spatio-temporal domain collocation points are sampled without exact labels, which brings training difficulties. Thus the selection of collocation points and sampling methods are quite crucial in training PINNs. Existing sampling methods include fixed and dynamic types, and in the more popular latter one, sampling is usually controlled by PDE residual loss. We point out that it is not sufficient to only consider the residual loss in adaptive sampling and sampling should obey temporal causality. We further introduce temporal causality into adaptive sampling and propose a novel adaptive causal sampling method to improve the performance and efficiency of PINNs. Numerical experiments of several PDEs with high-order derivatives and strong nonlinearity, including Cahn Hilliard and KdV equations, show that the proposed sampling method can improve the performance of PINNs with few collocation points. We demonstrate that by utilizing such a relatively simple sampling method, prediction performance can be improved up to two orders of magnitude compared with state-of-the-art results with almost no extra computation cost, especially when points are limited.
Learning world models from their sensory inputs enables agents to plan for actions by imagining their future outcomes. World models have previously been shown to improve sample-efficiency in simulated environments with few objects, but have not yet been applied successfully to environments with many objects. In environments with many objects, often only a small number of them are moving or interacting at the same time. In this paper, we investigate integrating this inductive bias of sparse interactions into the latent dynamics of world models trained from pixels. First, we introduce Variational Sparse Gating (VSG), a latent dynamics model that updates its feature dimensions sparsely through stochastic binary gates. Moreover, we propose a simplified architecture Simple Variational Sparse Gating (SVSG) that removes the deterministic pathway of previous models, resulting in a fully stochastic transition function that leverages the VSG mechanism. We evaluate the two model architectures in the BringBackShapes (BBS) environment that features a large number of moving objects and partial observability, demonstrating clear improvements over prior models.
Physics-informed neural networks (PINNs) have been widely applied in different fields due to their effectiveness in solving partial differential equations (PDEs). However, the accuracy and efficiency of PINNs need to be considerably improved for scientific and commercial use. To address this issue, we systematically propose a novel dimension-augmented physics-informed neural network (DaPINN), which simultaneously and significantly improves the accuracy and efficiency of the PINN. In the DaPINN model, we introduce inductive bias in the neural network to enhance network generalizability by adding a special regularization term to the loss function. Furthermore, we manipulate the network input dimension by inserting additional sample features and incorporating the expanded dimensionality in the loss function. Moreover, we verify the effectiveness of power series augmentation, Fourier series augmentation and replica augmentation, in both forward and backward problems. In most experiments, the error of DaPINN is 1$\sim$2 orders of magnitude lower than that of PINN. The results show that the DaPINN outperforms the original PINN in terms of both accuracy and efficiency with a reduced dependence on the number of sample points. We also discuss the complexity of the DaPINN and its compatibility with other methods.
Vast amount of data generated from networks of sensors, wearables, and the Internet of Things (IoT) devices underscores the need for advanced modeling techniques that leverage the spatio-temporal structure of decentralized data due to the need for edge computation and licensing (data access) issues. While federated learning (FL) has emerged as a framework for model training without requiring direct data sharing and exchange, effectively modeling the complex spatio-temporal dependencies to improve forecasting capabilities still remains an open problem. On the other hand, state-of-the-art spatio-temporal forecasting models assume unfettered access to the data, neglecting constraints on data sharing. To bridge this gap, we propose a federated spatio-temporal model -- Cross-Node Federated Graph Neural Network (CNFGNN) -- which explicitly encodes the underlying graph structure using graph neural network (GNN)-based architecture under the constraint of cross-node federated learning, which requires that data in a network of nodes is generated locally on each node and remains decentralized. CNFGNN operates by disentangling the temporal dynamics modeling on devices and spatial dynamics on the server, utilizing alternating optimization to reduce the communication cost, facilitating computations on the edge devices. Experiments on the traffic flow forecasting task show that CNFGNN achieves the best forecasting performance in both transductive and inductive learning settings with no extra computation cost on edge devices, while incurring modest communication cost.
Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and content information, and several recent methods based on it have achieved promising clustering performance on some real attributed networks. However, there is limited understanding of how graph convolution affects clustering performance and how to properly use it to optimize performance for different graphs. Existing methods essentially use graph convolution of a fixed and low order that only takes into account neighbours within a few hops of each node, which underutilizes node relations and ignores the diversity of graphs. In this paper, we propose an adaptive graph convolution method for attributed graph clustering that exploits high-order graph convolution to capture global cluster structure and adaptively selects the appropriate order for different graphs. We establish the validity of our method by theoretical analysis and extensive experiments on benchmark datasets. Empirical results show that our method compares favourably with state-of-the-art methods.
Humans and animals have the ability to continually acquire, fine-tune, and transfer knowledge and skills throughout their lifespan. This ability, referred to as lifelong learning, is mediated by a rich set of neurocognitive mechanisms that together contribute to the development and specialization of our sensorimotor skills as well as to long-term memory consolidation and retrieval. Consequently, lifelong learning capabilities are crucial for autonomous agents interacting in the real world and processing continuous streams of information. However, lifelong learning remains a long-standing challenge for machine learning and neural network models since the continual acquisition of incrementally available information from non-stationary data distributions generally leads to catastrophic forgetting or interference. This limitation represents a major drawback for state-of-the-art deep neural network models that typically learn representations from stationary batches of training data, thus without accounting for situations in which information becomes incrementally available over time. In this review, we critically summarize the main challenges linked to lifelong learning for artificial learning systems and compare existing neural network approaches that alleviate, to different extents, catastrophic forgetting. We discuss well-established and emerging research motivated by lifelong learning factors in biological systems such as structural plasticity, memory replay, curriculum and transfer learning, intrinsic motivation, and multisensory integration.
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