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Exact operator inference with minimal data
Get PDFThis work introduces a novel method to generate snapshot data for operator inference that guarantees the exact reconstruction of intrusive projection-based reduced-order models (ROMs). To ensure exact reconstruction, the operator inference least squares matrix must have full rank, without regularization. Existing works have achieved this full rank using heuristic strategies to generate snapshot data and a-posteriori checks on full rank, but without a guarantee of success. Our novel snapshot data generation method provides this guarantee thanks to two key ingredients: first we identify ROM states that induce full rank, then we generate snapshots corresponding to exactly these states by simulating multiple trajectories for only a single time step. This way, the number of required snapshots is minimal and orders of magnitude lower than typically reported with existing methods. The method avoids non-Markovian terms and does not require re-projection. Since the number of snapshots is minimal, the least squares problem simplifies to a linear system that is numerically more stable. In addition, because the inferred operators are exact, properties of the intrusive ROM operators such as symmetry or skew-symmetry are preserved. Numerical results for differential equations involving 2nd, 3rd and 8th order polynomials demonstrate that the novel snapshot data generation method leads to exact reconstruction of the intrusive reduced order models
SPIRIT Open Call 1 Winners: Interview with Irene Viola from Centrum Wiskunde en Informatica & MotionSpell
No full textInterview with Irene Viola and her winning proposal OPEN-DASH-PC: Open-Source ULL-DASH-PC For Multi-Party Real-Time Communicatio
Enhancing the audience experience for VR and AR theatre with AI-generated subtitles
Get PDFRecent technological developments on AI and immersive media are transforming the artistic landscape, providing novel mechanisms for artists and audiences. Following a human-centric approach, together with a theatre company in Greece, this paper investigates how subtitle placement affects user experience and cognitive load in a live theatre performance enhanced by AR glasses. To do so, we design and develop a system for displaying subtitles in VR and AR. We evaluated the system in two conditions (N = 19;N = 12), both in a controlled environment (VR) and an actual theatre (AR). In the latter, we integrate AI solutions to provide automatic captioning and translation in real time, and VFX to further augment the experience. Our quantitative and qualitative results showed no difference between subtitle placements in terms of cognitive load and user experience, with users equally liking the two proposed approaches. Results also highlighted the perceived usefulness of AR to enhance theatre performances, indicating new paths for wider accessibility and further immersion
Multi-patch isogeometric neural solver for partial differential equations on computer-aided design domains
Get PDFThis work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes patch-local neural networks that operate on the reference domain of isogeometric analysis. A custom output layer enables the strong imposition of Dirichlet boundary conditions. Solution conformity across interfaces between non-uniform rational B-spline patches is enforced using dedicated interface neural networks. Training is performed using the variational framework by minimizing the energy functional derived after the weak form of the partial differential equation. The effectiveness of the suggested method is demonstrated on two highly non-trivial and practically relevant use-cases, namely, a 2D magnetostatics model of a quadrupole magnet and a 3D nonlinear solid and contact mechanics model of a mechanical holder. The results show excellent agreement to reference solutions obtained with high-fidelity finite element solvers, thus highlighting the potential of the suggested neural solver to tackle complex engineering problems given the corresponding computer-aided design models
Novelty in Monte Carlo tree search
Get PDFNovelty search has shown benefits in different fields such as evolutionary computing, classical AI planning, and deep reinforcement learning. Searching for novelty instead of, or in addition to, directly maximizing the search objective, aims at avoiding dead ends and local minima, and overall improving exploration. We propose and test the integration of novelty into Monte Carlo Tree Search (MCTS), a popular framework for online RL planning, by linearly combining value estimates with novelty scores during the selection phase of MCTS. We adapt four different novelty measures from the literature (evaluation novelty, state-pseudocounts, feature-pseudocounts, and frequency-thresholding), integrate them into MCTS, and test them in six board games (Connect4, Othello, Breakthrough, Knightthrough, AtariGo and Gomoku). Experiments show improvements for MCTS in a wide range of settings, covering both guidance by handcoded heuristics and neural networks. The results demonstrate potential for these optimistic novelty estimates to achieve online generalisation of uncertainty during search
agdestein / ExactClosure.jl
No full textSource code for the paper "Exact closure for discrete large-eddy simulation"
Anti-concentration is (almost) all you need
Get PDFUntil very recently, it was generally believed that the (approximate) 2-design property is strictly stronger than anti-concentration of random quantum circuits, mainly because it was shown that the latter anti-concentrate in logarithmic depth, while the former generally need linear depth circuits. This belief was disproven by recent results which show that so-called relative-error approximate unitary designs can in fact be generated in logarithmic depth, implying anti-concentration. Their result does however not apply to ordinary local random circuits, a gap which we close in this letter, at least for 2-designs. More precisely, we show that anti-concentration of local random quantum circuits already implies that they form relative-error approximate state 2-designs, making them equivalent properties for these ensembles. Our result holds more generally for any random circuit which is invariant under local (single-qubit) unitaries, independent of the architecture
Hidden shift problem for complex functions
Get PDFWe study quantum algorithms for the hidden shift problem of complex scalar- and vector-valued functions on finite abelian groups. Given oracle access to a shifted function and the Fourier transform of the unshifted function, the goal is to find the hidden shift. We analyze the success probability of our algorithms when using a constant number of queries. For bent functions, they succeed with probability 1, while for arbitrary functions the success probability depends on the 'bentness' of the function
Relative phase equivariant deep neural systems for physical layer communications
Get PDFIn the era of telecommunications, the increasing demand for complex and specialized communication systems has led to a focus on improving physical layer communications. Artificial intelligence (AI) has emerged as a promising solution avenue for doing so. Deep neural receivers have already shown significant promise in improving the performance of communications systems. However, a major challenge lies in developing deep neural receivers that match the energy efficiency and speed of traditional receivers. This work investigates the incorporation of inductive biases in the physical layer using group-equivariant deep learning to improve the parameter efficiency of deep neural receivers. We do so by constructing a deep neural receiver that is equivariant with respect to the phase of arrival. We show that the inclusion of relative phase equivariance significantly reduces the error rate of deep neural receivers at similar model sizes. Thus, we show the potential of group-equivariant deep learning in the domain of physical layer communications