arXiv subjects

A. Pedro Aguiar

Publications and source records attributed to A. Pedro Aguiar.

At least 19 recordsLinked to original sources

arXiv2026

On Embedding Design in Quantum Physics-Informed Neural Networks

Quantum physics-informed neural networks (QPINNs) solve partial differential equations (PDEs) by training parameterized quantum circuits against physics-based residuals, yet the role of the embedding that maps coordinates into quantum states remains insufficiently understood. In this research, we introduce a unified embedding framework that formulates embedding as a functional transformation shaping the feature representation available to the variational circuit, and we propose two embeddings within it. The Linear Quantum Neural Network Trainable Embedding QPINN (LQNN-TE-QPINN) generates data-dependent features with an auxiliary quantum circuit and adds them to the input coordinates, instead of multiplying them as in our previous formulation. The adaptive-frequency QPINN (AdaFreq-QPINN) promotes the frequency-scaling factors of an arccos-Chebyshev encoding to trainable parameters. We evaluate both against direct and fixed analytical frequency encodings and alternative hybrid architectures on one- and two-dimensional Burgers equations. In one dimension, LQNN-TE-QPINN achieves a relative $L_2$ error of 0.0916 with 720 trainable parameters, compared with 0.4501 for direct-encoding QPINN and 0.1233 for a locally adaptive classical physics-informed neural network with approximately eleven times more parameters, while AdaFreq-QPINN attains the lowest error among the analytical embeddings with only four additional parameters. In two dimensions, LQNN-TE-QPINN attains the lowest training objective, although its solution error is not clearly separated from that of a data re-uploading QPINN. Under simulated hardware noise, LQNN-TE-QPINN retains the lowest absolute derivative error while degrading most relative to its noiseless baseline. These results demonstrate that embedding design substantially influences the approximation and optimization behavior of QPINNs.

quant-ph↗

arXiv2026

Learning-Based Dynamic Obstacle Avoidance for a UAV Using Only Three Range Sensors

We present a learning-based approach to kinodynamic online motion planning for an Unmanned Aerial Vehicle (UAV) operating at a fixed altitude in unknown dynamic environments, where real-time avoidance of both static and dynamic obstacles must be achieved under conditions of extreme partial observability. The UAV is controlled with a single degree of freedom (yaw only), resulting in constrained, nonholonomic motion similar to fixed-wing platforms. The proposed framework integrates a behavior grid map representation with Deep Reinforcement Learning (DRL), using Proximal Policy Optimization (PPO) for stable policy learning in continuous control. The key idea is the co-design of a state representation and control policy that enables reliable navigation using only three low-cost directional range sensors, without reliance on dense sensing modalities such as LiDAR or vision-based systems. The behavior grid map dynamically aggregates sparse measurements into a structured local representation that supports real-time decision-making for obstacle avoidance and target reaching. Extensive simulations across environments of varying sizes and obstacle densities demonstrate that the proposed standard and enhanced methods achieve higher success rates than PPO variants and Model Predictive Control (MPC) (94\% vs. 79--90\% in small-scale high-congestion scenarios, and 83\% vs. 62--71\% in large-scale high-congestion scenarios), while maintaining real-time performance. Real-world experiments across four scenarios further confirm practical feasibility, with consistent target-reaching behaviour and no collisions under the tested conditions.

cs.RO↗

arXiv2026

Rank-Dependent Error Bounds and Near-Optimality in Quantum Control via Hierarchical Tucker Surrogates

We develop a certified finite-horizon quantum optimal-control framework based on fixed-rank Hierarchical Tucker (HT) surrogates. Under a uniform rank-dependent HT truncation-accuracy condition, we establish exponentially decaying trajectory, cost, and value-function errors and near-optimality of surrogate-generated controls. We further derive a logarithmic rank--performance relation, an a posteriori cost certificate from realized truncation perturbations, and guarantees for inexact surrogate optimization and control convergence under additional regularity conditions. Numerical experiments on controlled XXZ spin chains provide finite-sample evidence consistent with the truncation condition and illustrate the trade-off between HT rank, representation size, surrogate accuracy, and control performance.

math.OC↗

arXiv2026

Efficient Audio-Visual Event Recognition via Knowledge Distillation and Dynamic INT8 Quantization of a Hybrid Cross-Attention Network

Audio-visual event recognition (AVER) has achieved significant performance improvements through transformer-based multimodal architectures. However, the high computational complexity, large memory footprint, and inference cost of these models hinder their deployment on edge and resource-constrained devices. This paper presents an efficient compression framework for hybrid cross-attention-based audiovisual event recognition by combining architectural model compression, knowledge distillation, and dynamic INT8 quantization. A high-capacity teacher model integrates VideoMAE for visual representation learning, the Audio Spectrogram Transformer (AST) for audio feature extraction, and a hybrid cross-attention fusion network for multimodal feature integration. A lightweight student model is constructed by reducing the hidden feature dimension, the number of attention heads, and the feedforward network size while preserving the overall network architecture. The student model is trained using knowledge distillation to effectively transfer discriminative knowledge from the teacher. Finally, dynamic INT8 post-training quantization is applied to further reduce the model size for efficient deployment. Experimental results on the Audio-Visual Event (AVE) dataset show that the proposed framework reduces the number of trainable parameters in the multimodal fusion module by 59.06%, with only a 2.14% decrease in classification accuracy compared with the teacher model. Furthermore, dynamic INT8 quantization reduces the model size from 10.71 MB to 2.04 MB while maintaining competitive recognition performance. These results demonstrate that the proposed framework provides an effective trade-off between recognition accuracy and computational efficiency, making it a promising solution for deployment on resource-constrained edge AI platforms.

eess.SP↗

arXiv2026

A Variational Surrogate Approach to Finite-Horizon Quantum Control via Hardware-Efficient Ansatz

We present a variational quantum framework for finite-horizon quantum control based on hardware-efficient ansätze. The objective is to steer a quantum system from a given initial state to a desired target state over a fixed time horizon by minimizing a terminal cost defined in terms of state fidelity. Instead of explicitly synthesizing time-dependent control fields or enforcing Hamiltonian reachability constraints, the proposed method reformulates the control objective as a variational optimization problem in which a hardware-efficient parameterized quantum circuit provides a surrogate parameterization of the terminal evolution. The circuit consists of alternating layers of single-qubit rotations and entangling gates, whose parameters are optimized using classical routines to minimize the terminal infidelity. This formulation avoids reliance on problem-specific or physics-inspired ansätze, providing a flexible and implementation-friendly approach compatible with near-term quantum devices. Numerical experiments on multi-qubit state-transfer benchmarks demonstrate high-fidelity state transfer while highlighting the trade-off between ansatz expressivity, optimization complexity, and scalability with respect to system size and circuit depth.

quant-ph↗

arXiv2026

Tensor Network Methods for Advection-Diffusion-Reaction Systems Using Quantum-Inspired Representations

We present a quantum-inspired tensor-network framework for solving advection-diffusion-reaction (ADR) partial differential equations. Discretized solution fields are encoded as matrix product states (MPS), while differential operators are represented as matrix product operators (MPOs). Time integration is performed entirely in tensor-network form using explicit Euler updates with controlled truncation. The method is evaluated on one- and two-dimensional ADR problems and compared with high-accuracy Runge-Kutta reference solutions. Numerical results show that the proposed representation remains compact, stable, and accurate across a range of dynamical regimes. The solver captures both local solution profiles and global observables while maintaining small bond dimensions throughout the simulation. These results highlight the potential of tensor networks as efficient structure-preserving tools for PDE simulation in multiple spatial dimensions.

math.NA↗

arXiv2026

Stable Hybrid Cross-Attention Fusion for Audio-Visual Event Recognition

Audio-Visual Event Recognition (AVER) is essential for intelligent urban monitoring systems, where robust multimodal understanding of complex environments is required. This paper proposes a stable hybrid cross-attention fusion framework for audio-visual event recognition in smart urban environments. The proposed architecture combines pretrained Video Masked Autoencoder (VideoMAE) and Audio Spectrogram Transformer (AST) representations with FiLM-based audio conditioning, bidirectional cross-attention fusion, multimodal Transformer encoding, and modality-temporal attention. To improve computational efficiency and training stability, frozen pretrained backbones and cached feature extraction are employed. Extensive experiments on the AVE dataset show that the proposed framework achieves the highest average performance among the evaluated unimodal and multimodal baselines across multiple evaluation metrics, obtaining a best validation accuracy of 91.74% and a test accuracy of 83.85 plus/minus 1.40% over five independent runs. The results indicate that the proposed hybrid fusion strategy effectively captures complementary audio-visual information and provides robust multimodal representation learning for challenging realworld urban monitoring scenarios.

eess.AS↗

arXiv2026

A QPINN Framework with Quantum Trainable Embeddings for the Lid-Driven Cavity Problem

The steady incompressible Navier--Stokes equations pose significant computational challenges due to their nonlinear convective terms and pressure--velocity coupling. Physics-informed neural networks (PINNs) provide a mesh-free framework for approximating such systems, but classical PINNs can experience optimization difficulties in nonlinear flow regimes. In this work, we propose a quantum physics-informed neural network (QPINN) framework with a quantum neural network (QNN)-based trainable embedding for the lid-driven cavity problem. The proposed approach uses a QNN to learn data-adaptive quantum feature maps that encode spatial coordinates before they are processed by a variational quantum circuit within a physics-informed loss formulation. Numerical experiments show that the proposed QNN-TE-QPINN exhibits stable training behavior and competitive solution accuracy compared with classical PINNs and hybrid quantum models using classical embeddings, while requiring significantly fewer trainable parameters. Rather than claiming computational speedup, these results highlight the potential of trainable quantum embeddings for parameter-efficient physics-informed learning. The findings suggest that embedding design plays an important role in quantum-assisted PDE solvers and support further investigation of QNN-based trainable embeddings for nonlinear fluid dynamics benchmarks.

quant-ph↗

arXiv2026

Robust Adaptive Backstepping Impedance Control of Robots in Unknown Environments

This paper presents a Robust Adaptive Backstepping Impedance Control (RABIC) strategy for robots operating in contact-rich and uncertain environments. The proposed control strategy considers the complete coupled dynamics of the system and explicitly accounts for key sources of uncertainty, including external disturbances and unmodeled dynamics, while not requiring the robot's dynamic parameters in implementation. We propose a backstepping-based adaptive impedance control scheme for the inner loop to track the reference impedance model. To handle uncertainties, we employ a Taylor series-based estimator for system dynamics and an adaptive estimator for determining the upper bound of external forces. Stability analysis demonstrates the semi-global practical finite-time stability of the overall system. To demonstrate the effectiveness of the proposed method, a simulated mobile manipulator scenario and experimental evaluations on a real Franka Emika Panda robot were conducted. The proposed approach exhibits safer performance compared to PD control while ensuring trajectory tracking and force monitoring. Overall, the RABIC framework provides a solid basis for future research on adaptive and learning-based impedance control for coupled mobile and fixed serially linked manipulators.

cs.RO↗

arXiv2026

Certified Quantum Schrödinger Control via Hierarchical Tucker Models

High-dimensional Schrödinger systems arising from tensor-product discretizations suffer from exponential state growth, making direct controller synthesis and real-time closed-loop simulation computationally challenging. Hierarchical Tucker (HT) tensor representations offer scalable low-rank surrogates, but the impact of fixed-rank truncation on closed-loop stability is not well understood. This paper develops a local robustness framework for sampled-data feedback control implemented with fixed-rank HT projections. By viewing each truncation as a bounded, rank-dependent perturbation of the nominal closed loop, and assuming a local phase-invariant contraction certificate together with trajectory-level hierarchical spectral decay, we show that the HT-projected dynamics are practically exponentially stable: trajectories converge to a dimension-independent tube whose radius decreases with the prescribed rank. We further obtain an explicit logarithmic rank-accuracy relation and establish conditions under which controllers designed on the HT-truncated surrogate model retain practical exponential tracking guarantees when deployed on the full system, together with an explicit bound quantifying the resulting surrogate-to-plant mismatch. A compact lattice example demonstrates the applicability of the framework.

quant-ph↗

arXiv2026

Exact Cost-Increment Formula for Optimal Control of Semilinear Evolution Equations

We address optimal control of semilinear evolution equations on Banach spaces with finitely many control channels, a framework encompassing a broad class of infinite-dimensional dynamical systems, arising in many applications. For this setting, we derive an exact and global formula quantifying the increment of the cost functional with respect to an arbitrary reference control. This identity enables the design of monotone descent algorithms that require no linearization or step-size tuning. We further establish the existence of optimal controls and propose a practical sample-and-hold realization of the descent step suitable for numerical implementation. The effectiveness of the method is demonstrated on a controlled reaction-diffusion equation.

math.OC↗

arXiv2026

On the Stability of Undesirable Equilibria in the Quadratic Program Framework for Safety-Critical Control

Control Lyapunov functions (CLFs) and Control Barrier Functions (CBFs) have been used to develop provably safe controllers by means of quadratic programs (QPs). This framework guarantees safety in the form of trajectory invariance with respect to a given set, but it can introduce undesirable equilibrium points to the closed loop system, which can be asymptotically stable. In this work, we present a detailed study of the formation and stability of equilibrium points with the CLF-CBF-QP framework with multiple CBFs. In particular, we prove that undesirable equilibrium points occur for most systems, and their stability is dependent on the CLF and CBF geometrical properties. We introduce the concept of CLF-CBF compatibility for a system, regarding a CLF-CBF pair inducing no stable equilibrium points other than the CLF global minimum on the corresponding closed-loop dynamics. Sufficient conditions for CLF-CBF compatibility for LTI and drift-less full-rank systems with quadratic CLF and CBFs are derived, and we propose a novel control strategy to induce smooth changes in the CLF geometry at certain regions of the state space in order to satisfy the CLF-CBF compatibility conditions, aiming to achieve safety with respect to multiple safety objectives and quasi-global convergence of the trajectories towards the CLF minimum. Numerical simulations illustrate the applicability of the proposed method.

eess.SY↗

arXiv2026

Evaluating CNN with Stacked Feature Representations and Audio Spectrogram Transformer Models for Sound Classification

Environmental sound classification (ESC) has gained significant attention due to its diverse applications in smart city monitoring, fault detection, acoustic surveillance, and manufacturing quality control. To enhance CNN performance, feature stacking techniques have been explored to aggregate complementary acoustic descriptors into richer input representations. In this paper, we investigate CNN-based models employing various stacked feature combinations, including Log-Mel Spectrogram (LM), Spectral Contrast (SPC), Chroma (CH), Tonnetz (TZ), Mel-Frequency Cepstral Coefficients (MFCCs), and Gammatone Cepstral Coefficients (GTCC). Experiments are conducted on the widely used ESC-50 and UrbanSound8K datasets under different training regimes, including pretraining on ESC-50, fine-tuning on UrbanSound8K, and comparison with Audio Spectrogram Transformer (AST) models pretrained on large-scale corpora such as AudioSet. This experimental design enables an analysis of how feature-stacked CNNs compare with transformer-based models under varying levels of training data and pretraining diversity. The results indicate that feature-stacked CNNs offer a more computationally and data-efficient alternative when large-scale pretraining or extensive training data are unavailable, making them particularly well suited for resource-constrained and edge-level sound classification scenarios.

eess.AS↗

arXiv2026

Quantum-Assisted Trainable-Embedding Physics-Informed Neural Networks for Parabolic PDEs

Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding governing physical laws directly into the training objective. Recent advances in quantum machine learning have motivated hybrid quantum-classical extensions aimed at enhancing representational capacity while remaining compatible with near-term quantum hardware. In this work, we investigate trainable embedding strategies within quantum-assisted PINNs for solving parabolic PDEs, using one- and two-dimensional heat equations as canonical benchmarks. We introduce two quantum-assisted architectures that differ in their embedding components. In the first approach, a classical feed-forward neural network generates trainable feature maps for quantum data encoding (FNN-TE-QPINN). In the second, the embedding stage is realized entirely by a parameterized quantum circuit (QNN-TE-QPINN), yielding a fully quantum feature map. Our findings emphasize the critical role of embedding design and support hybrid quantum-classical approaches for parabolic PDE modeling in the NISQ era.

quant-ph↗

arXiv2026

Quantum-Inspired Tensor Networks for Approximating PDE Flow Maps

We investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective low-rank structure that emerges after tensorization of discretized transport and diffusion dynamics, we encode PDE states as matrix product states (MPS) and represent the evolution operator as a structured low-rank matrix product operator (MPO) in tensor-train form (e.g., arising from finite-difference discretizations assembled in MPO form). The MPO is applied directly in MPS form, and rank growth is controlled via canonicalization and SVD-based truncation after each step. We provide theoretical context through standard matrix product properties, including exact MPS representability bounds, local optimality of SVD truncation, and a Lipschitz-type multi-step error propagation estimate. Experiments on one- and two-dimensional linear advection-diffusion and nonlinear viscous Burgers equations demonstrate accurate short-horizon prediction, favorable scaling in smooth diffusive regimes, and error growth in nonlinear multi-step predictions.

math.NA↗

arXiv2026

A Trainable-Embedding Quantum Physics-Informed Framework for Multi-Species Reaction-Diffusion Systems

Physics-informed neural networks (PINNs) and hybrid quantum-classical extensions provide a promising framework for solving partial differential equations (PDEs) by embedding physical laws directly into the learning process. In this work, we study embedding strategies for trainable embedding quantum physics-informed neural networks (TE-QPINNs) in the context of nonlinear reaction-diffusion (RD) systems. We introduce an extended TE-QPINN (x-TE-QPINN) architecture that supports both classical and fully quantum embeddings, enabling a controlled comparison between feedforward neural network-based feature maps and parameterized quantum circuit embeddings. The first architecture is the classical embedding feed-forward neural network-based TE-QPINN (FNN-TE-QPINN), while the latter variant is a purely quantum one, referred to as quantum embedding neural network-based TE-QPINN (QNN-TE-QPINN). The proposed framework employs hardware-efficient variational quantum circuits and species-specific readout operators to approximate coupled multi-field dynamics while enforcing governing equations, boundary conditions, and initial conditions through a physics-informed loss function. By isolating the embedding mechanism while keeping the variational ansatz, loss formulation, and optimization procedure fixed, we analyze the impact of embedding design on gradient structure, parameter scaling, and quantum resource requirements. Numerical experiments on one- and two-dimensional RD equations demonstrate that quantum embeddings can replace classical embeddings without degradation in solution accuracy and, in certain regimes, exhibit improved optimization behavior compared to classical PINNs and hybrid quantum models with fixed embeddings. These results provide architectural insight into hybrid quantum PDE solvers and inform the design of resource-efficient quantum physics-informed learning methods.

quant-ph↗

arXiv2025

Indirect methods in optimal control on Banach spaces

This work focuses on indirect descent methods for optimal control problems governed by nonlinear ordinary differential equations in Banach spaces, viewed as abstract models of distributed dynamics. As a reference line, we revisit the classical schemes, rooted in Pontryagin's maximum principle, and highlight their sensitivity to local convexity and lack of monotone convergence. We then develop an alternative method based on exact cost-increment formulas and finite-difference probes of the terminal cost. We show that our method exhibits stable monotone convergence in numerical analysis of an Amari-type neural field control problem.

math.OC↗

arXiv2025

Trotterized Variational Quantum Control for Spin-Chain State Transfer

We present a hybrid variational framework for quantum optimal control aimed at high-fidelity state transfer in spin chains. The system dynamics are discretized and compiled into a parameterized circuit, where deterministic two-qubit blocks implement the drift interactions, while trainable on-site RZ rotations encode the control inputs. We study two parameterizations: a compact global scheme with a small number of shared parameters per slice, and a local scheme with site-wise angles. Using a Sequential Least Squares Quadratic Programming (SLSQP) optimization to minimize infidelity, simulations on XXZ spin chains show that both parameterizations can achieve near-unit fidelities in the noiseless regime. Under depolarizing noise, the global scheme provides improved robustness for comparable circuit depth and iteration budgets. The results make explicit an expressivity-stability trade-off and suggest a scalable route to Noisy Intermediate-Scale Quantum (NISQ) compatible control synthesis.

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