Neural networks are powerful tools in various applications, and quantifying their uncertainty is crucial for reliable decision-making. In the deep learning field, the uncertainties are usually categorized into aleatoric (data) and epistemic (model) uncertainty. In this paper, we point out that the existing popular variance attenuation method highly overestimates aleatoric uncertainty. To address this issue, we proposed a new estimation method by actively de-noising the observed data. By conducting a broad range of experiments, we demonstrate that our proposed approach provides a much closer approximation to the actual data uncertainty than the standard method.

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named $\textbf{ConCerNet}$ to improve the trustworthiness of the DNN based dynamics modeling to endow the invariant properties. $\textbf{ConCerNet}$ consists of two steps: (i) a contrastive learning method to automatically capture the system invariants (i.e. conservation properties) along the trajectory observations; (ii) a neural projection layer to guarantee that the learned dynamics models preserve the learned invariants. We theoretically prove the functional relationship between the learned latent representation and the unknown system invariant function. Experiments show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics by a large margin. With neural network based parameterization and no dependence on prior knowledge, our method can be extended to complex and large-scale dynamics by leveraging an autoencoder.

Recent studies have shown that deep reinforcement learning agents are vulnerable to small adversarial perturbations on the agent's inputs, which raises concerns about deploying such agents in the real world. To address this issue, we propose RADIAL-RL, a principled framework to train reinforcement learning agents with improved robustness against $l_p$-norm bounded adversarial attacks. Our framework is compatible with popular deep reinforcement learning algorithms and we demonstrate its performance with deep Q-learning, A3C and PPO. We experiment on three deep RL benchmarks (Atari, MuJoCo and ProcGen) to show the effectiveness of our robust training algorithm. Our RADIAL-RL agents consistently outperform prior methods when tested against attacks of varying strength and are more computationally efficient to train. In addition, we propose a new evaluation method called Greedy-Worst-Case Reward (GWC) to measure attack agnostic robustness of deep RL agents. We show that GWC can be evaluated efficiently and is a good estimate of the reward under the worst possible sequence of adversarial attacks. All code used for our experiments is available at https://github.com/tuomaso/radial_rl_v2.

In this paper, we propose a power encoding method for converting a high-resolution OFDM baseband signal into a signal that assumes only a finite number of values. This is achieved by the series interconnection of, optimally (co)designed, delta- sigma (/spl Delta/ /Spl Sigma/M) and digital pulse-width modulators (DPWM). Given an input signal class with a known mplitude distribution (e.g., OFDM), parameters of the multilevel DPWM are designed such that the mean squared error of the inherent DPWM quantization noise is inimized. Parameters of the /spl Delta/ /Spl Sigma/M are then chosen with respect to the designed DPWM, so to optimally shape the inherent quantization noise out of the spectral band of interest. The superior performance of the proposed novel power encoding scheme is demonstrated by Matlab simulations on several standardized LTE test signals.

In this paper we present a passive reduced order modeling algorithm for linear multiport interconnect structures. The proposed technique uses rational fitting via semidefinite programming to identify a passive transfer matrix from given frequency domain data samples. Numerical results are presented for a power distribution grid and an array of inductors, and the proposed approach is compared to two existing rational fitting techniques.

This paper presents a system identification technique for generating stable compact models of typical analog circuit blocks in radio frequency systems. The identification procedure is based on minimizing the model error over a given training data set subject to an incremental stability constraint, which is formulated as a semidefinite optimization problem. Numerical results are presented for several analog circuits, including a distributed power amplifier, as well as a MEM device. It is also shown that our dynamical models can accurately predict important circuit performance metrics, and may thus, be useful for design optimization of analog systems.

In this paper, an optimization-based model order reduction (MOR) framework is proposed. The method involves setting up a quasi-convex program that solves a relaxation of the optimal${\cal H}_{\infty}$norm MOR problem. The method can generate guaranteed stable and passive reduced models and is very flexible in imposing additional constraints such as exact matching of specific frequency response samples. The proposed optimization-based approach is also extended to solve the parameterized model-reduction problem (PMOR). The proposed method is compared to existing moment matching and optimization-based MOR methods in several examples. PMOR models for large RF inductors over substrate and power-distribution grid are also constructed.

Typical nonlinear model order reduction ap- proaches need to address two issues: reducing the order of the model, and approximating the vector field. In this paper we focus exclusively on the second issue, and present results characterizing the repercussions at the system level of vector field approximations. The error assessment problem is formulated as the L2 gain upper bounding problem of a scaled feedback interconnection. Applying the small gain theorem in the proposed setup, we prove that the L2 gain of the error system is upper bounded by the L2 gain of the vector field approximation error, provided it is small. In addition, the paper also presents a numerical procedure, based on the IQC/LMI approach, to perform the error estimation task with less conservatism. A numerical example is given in this paper to demonstrate the practical implications of the presented results.

In this paper an optimization based model order reduction (MOR) framework is proposed. The method involves setting up a quasiconvex program that explicitly minimizes a relaxation of the optimal H∞ norm MOR problem. The method generates guaranteed stable and passive reduced models and it is very flexible in imposing additional constraints. The proposed optimization approach is also extended to parameterized model reduction problem (PMOR). The proposed method is compared to existing moment matching and optimization based MOR methods in several examples. A PMOR model for a large RF inductor is also constructed.

We develop a sufficient condition for the least-squares measurement (LSM), or the square-root measurement, to minimize the probability of a detection error when distinguishing between a collection of mixed quantum states. Using this condition we derive the optimal measurement for state sets with a broad class of symmetries. We first consider geometrically uniform (GU) state sets with a possibly non-Abelian generating group, and show that if the generator satisfies a weighted norm constraint, then the LSM is optimal. In particular, for pure-state GU ensembles, the LSM is shown to be optimal. For arbitrary GU state sets we show that the optimal measurement operators are GU with generator that can be computed very efficiently in polynomial time, within any desired accuracy. We then consider compound GU (CGU) state sets which consist of subsets that are GU. When the generators satisfy a certain constraint, the LSM is again optimal. For arbitrary CGU state sets, the optimal measurement operators are shown to be CGU with generators that can be computed efficiently in polynomial time.

We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing among a collection of quantum states, represented by a set of density operators. We show that the design of the optimal detector can be formulated as a semidefinite programming problem. Based on this formulation, we derive a set of necessary and sufficient conditions for an optimal quantum measurement. We then show that the optimal measurement can be found by solving a standard (convex) semidefinite program. By exploiting the many well-known algorithms for solving semidefinite programs, which are guaranteed to converge to the global optimum, the optimal measurement can be computed very efficiently in polynomial time within any desired accuracy. Using the semidefinite programming formulation, we also show that the rank of each optimal measurement operator is no larger than the rank of the corresponding density operator. In particular, if the quantum state ensemble is a pure-state ensemble consisting of (not necessarily independent) rank-one density operators, then we show that the optimal measurement is a pure-state measurement consisting of rank-one measurement operators.