In this paper, we focus on SCI recovery algorithms that employ untrained neural networks (UNNs), such as deep image prior (DIP), to model source structure.

Many differentially private algorithms for answering database queries involve astep that reconstructs a discrete data distribution from noisy measurements. Thisprovides consistent query answers and reduces error, but often requires space thatgrows exponentially with dimension. PRIVATE-PGM is a recent approach that usesgraphical models to represent the data distribution, with complexity proportional tothat of exact marginal inference in a graphical model with structure determined bythe co-occurrence of variables in the noisy measurements. PRIVATE-PGM is highlyscalable for sparse measurements, but may fail to run in high dimensions with densemeasurements. We overcome the main scalability limitation of PRIVATE-PGMthrough a principled approach that relaxes consistency constraints in the estimationobjective. Our new approach works with many existing private query answeringalgorithms and improves scalability or accuracy with no privacy cost.

The proof of Theorem 4.2 in the main paper uses the following technical lemma: The proof of Lemma 1.1 follows standard covering arguments and may be sketched as follows. Full details can be found in the proofs in [1].We can now present the proof of Theorem 4.2: Proof. We end this section with the proof of Proposition 4.3 in the main paper: Proof. Algorithm 1 provides the pseudo-code of the proposed multi-operator imaging (MOI) method. Figure 1: The residual U-Net used in the paper.

This study presents a physics-informed machine learning-based control method for nonlinear dynamic systems with highly noisy measurements. Existing data-driven control methods that use machine learning for system identification cannot effectively cope with highly noisy measurements, resulting in unstable control performance. To address this challenge, the present study extends current physics-informed machine learning capabilities for modeling nonlinear dynamics with control and integrates them into a model predictive control framework. To demonstrate the capability of the proposed method we test and validate with two noisy nonlinear dynamic systems: the chaotic Lorenz 3 system, and turning machine tool. Analysis of the results illustrate that the proposed method outperforms state-of-the-art benchmarks as measured by both modeling accuracy and control performance for nonlinear dynamic systems under high-noise conditions.

Hamiltonian neural networks (HNNs) represent a promising class of physics-informed deep learning methods that utilize Hamiltonian theory as foundational knowledge within neural networks. However, their direct application to engineering systems is often challenged by practical issues, including the presence of external inputs, dissipation, and noisy measurements. This paper introduces a novel framework that enhances the capabilities of HNNs to address these real-life factors. We integrate port-Hamiltonian theory into the neural network structure, allowing for the inclusion of external inputs and dissipation, while mitigating the impact of measurement noise through an output-error (OE) model structure. The resulting output error port-Hamiltonian neural networks (OE-pHNNs) can be adapted to tackle modeling complex engineering systems with noisy measurements. Furthermore, we propose the identification of OE-pHNNs based on the subspace encoder approach (SUBNET), which efficiently approximates the complete simulation loss using subsections of the data and uses an encoder function to predict initial states. By integrating SUBNET with OE-pHNNs, we achieve consistent models of complex engineering systems under noisy measurements. In addition, we perform a consistency analysis to ensure the reliability of the proposed data-driven model learning method. We demonstrate the effectiveness of our approach on system identification benchmarks, showing its potential as a powerful tool for modeling dynamic systems in real-world applications.

We derive a novel generative model from the simple act of Gaussian posterior inference. Treating the generated sample as an unknown variable to infer lets us formulate the sampling process in the language of Bayesian probability. Our model uses a sequence of prediction and posterior update steps to narrow down the unknown sample from a broad initial belief. In addition to a rigorous theoretical analysis, we establish a connection between our model and diffusion models and show that it includes Bayesian Flow Networks (BFNs) as a special case. In our experiments, we demonstrate improved performance over both BFNs and Variational Diffusion Models, achieving competitive likelihood scores on CIFAR10 and ImageNet.

Many differentially private algorithms for answering database queries involve astep that reconstructs a discrete data distribution from noisy measurements. Thisprovides consistent query answers and reduces error, but often requires space thatgrows exponentially with dimension. PRIVATE-PGM is a recent approach that usesgraphical models to represent the data distribution, with complexity proportional tothat of exact marginal inference in a graphical model with structure determined bythe co-occurrence of variables in the noisy measurements. PRIVATE-PGM is highlyscalable for sparse measurements, but may fail to run in high dimensions with densemeasurements. We overcome the main scalability limitation of PRIVATE-PGMthrough a principled approach that relaxes consistency constraints in the estimationobjective.

In this paper, we tackle the problem of localizing the source of a three-dimensional signal field with a team of mobile robots able to collect noisy measurements of its strength and share information with each other. The adopted strategy is to cooperatively compute a closed-form estimation of the gradient of the signal field that is then employed to steer the multi-robot system toward the source location. In order to guarantee an accurate and robust gradient estimation, the robots are placed on the surface of a sphere of fixed radius. More specifically, their positions correspond to the generators of a constrained Centroidal Voronoi partition on the spherical surface. We show that, by keeping these specific formations, both crucial geometric properties and a high level of field coverage are simultaneously achieved and that they allow estimating the gradient via simple analytic expressions. We finally provide simulation results to evaluate the performance of the proposed approach, considering both noise-free and noisy measurements. In particular, a comparative analysis shows how its higher robustness against faulty measurements outperforms an alternative state-of-the-art solution.