Given a source and a target probability measure, the Monge problem studies efficient ways to map the former onto the latter. This efficiency is quantified by defining a cost function between source and target data.

However, on-body displacement of sensors is inevitable since the device cannot be firmly worn at a fixed position across different sessions.

Our innovations dramatically improve accuracy over SOTA on standard flow benchmarks while being significantly easier to work with - training converges in 7X fewer iterations. Interestingly, our networks appear to generalize across diverse correspondence tasks. On-the-fly adaptation of search windows allows ustorepurpose optical flownetworks for stereo (and vice versa), and can also beused toimplement adapativenetworks that increase search windowsizeson-demand.

Neural Information Processing Systems http://nips.cc/

Conditional Value-at-Risk (CVaR) is a central tail-risk measure in stochastic structural mechanics, yet its accurate evaluation under high-dimensional, spatially correlated material uncertainty remains computationally prohibitive for classical Monte Carlo methods. Leveraging bounded-expectation reformulations of CVaR compatible with quantum amplitude estimation, we develop a quantum-enhanced inference framework that casts CVaR evaluation as a statistically consistent, confidence-constrained maximum-likelihood amplitude estimation problem. The proposed method extends iterative quantum amplitude estimation (IQAE) by embedding explicit maximum-likelihood inference within a rigorously controlled interval-tracking architecture. To ensure global correctness under finite-shot noise and the non-injective oscillatory response induced by Grover amplification, we introduce a stabilized inference scheme incorporating multi-hypothesis feasibility tracking, periodic low-depth disambiguation, and a bounded restart mechanism governed by an explicit failure-probability budget. This formulation preserves the quadratic oracle-complexity advantage of amplitude estimation while providing finite-sample confidence guarantees and reduced estimator variance. The framework is demonstrated on benchmark problems with spatially correlated lognormal Young's modulus fields generated using a Nystrom low-rank Gaussian kernel model. Numerical results show that the proposed estimator achieves substantially lower oracle complexity than classical Monte Carlo CVaR estimation at comparable confidence levels, while maintaining rigorous statistical reliability. This work establishes a practically robust and theoretically grounded quantum-enhanced methodology for tail-risk quantification in stochastic continuum mechanics.

To address this, we leverage parametric modular structure to learn component-level surrogates, enabling cheaper high-fidelity simulation. We use a neural network to model the stored potential energy in a component given boundary conditions.