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Deep learning models are defined in terms of a large number of hyperparameters, such as network architectures and optimiser settings. These hyperparameters must be determined separately from the model parameters such as network weights, and are often fixed by ad-hoc methods or by manual inspection of the results. An algorithmic, objective determination of hyperparameters demands the introduction of dedicated target metrics, different from those adopted for the model training. Here we present a new approach to the automated determination of hyperparameters in deep learning models based on statistical estimators constructed from an ensemble of models sampling the underlying probability distribution in model space. This strategy requires the simultaneous parallel training of up to several hundreds of models and can be effectively implemented by deploying hardware accelerators such as GPUs. As a proof-of-concept, we apply this method to the determination of the partonic substructure of the proton within the NNPDF framework and demonstrate the robustness of the resultant model uncertainty estimates. The new GPU-optimised NNPDF code results in a speed-up of up to two orders of magnitude, a stabilisation of the memory requirements, and a reduction in energy consumption of up to 90% as compared to sequential CPU-based model training. While focusing on proton structure, our method is fully general and is applicable to any deep learning problem relying on hyperparameter optimisation for an ensemble of models., Comment: 27 pages, 7 figures

Infections diseases are marked by recovering time distributions which can be far from the exponential one associated with Markovian/Poisson processes, broadly applied in epidemic compartmental models. In the present work, we tackled this problem by investigating a susceptible-infected-recovered-susceptible model on networks with $\eta$ independent infectious compartments (SI$_{\eta}$RS), each one with a Markovian dynamics, that leads to a Gamma-distributed recovering times. We analytically develop a theory for the epidemic lifespan on star graphs with a center and $K$ leaves showing that the epidemic lifespan scales with a non-universal power-law $\tau_{K}\sim K^{\alpha/\mu\eta}$ plus logarithm corrections, where $\alpha^{-1}$ and $\mu^{-1}$ are the mean waning immunity and recovering times, respectively. Compared with standard SIRS dynamics with $\eta=1$ and the same mean recovering time, the epidemic lifespan on star graphs is severely reduced as the number of stages increases. In particular, the case $\eta\rightarrow\infty$ leads to a finite lifespan. Numerical simulations support the approximated analytical calculations. For the SIS dynamics, numerical simulations show that the lifespan increases exponentially with the number of leaves, with a nonuniversal rate that decays with the number of infectious compartments. We investigated the SI$_{\eta}$RS dynamics on power-law networks with degree distribution $P(K)\sim k^{-\gamma}$. When $\gamma<5/2$, the epidemic spreading is ruled by a maximum $k$-core activation, the alteration of the hub activity time does not alter either the epidemic threshold or the localization pattern. For $\gamma>3$, where hub mutual activation is at work, the localization is reduced but not sufficiently to alter the threshold scaling with the network size. Therefore, the activation mechanisms remain the same as in the case of Markovian healing., Comment: 12 pages, 8 figures

We consider the focusing generalized Hartree equation in $H^1(\R^3)$ with a potential, \begin{equation*} iu_t + \Delta u - V(x)u + (I_\gamma \ast |u|^p )|u|^{p-2} u=0, \end{equation*} where $I_\gamma = \frac{1}{|x|^{3-\gamma}}$, $p \geq 2$ and $\gamma < 3$. In this paper, we prove scattering for the generalized Hartree equation with a potential in the intercritical case assuming radial initial data. The novelty of our approach lies in the use of a general mass-potential condition, incorporating the potential V, which extends the standard mass-energy framework. To this end, we employ a simplified method inspired by Dodson and Murphy \cite{Dod-Mur}, based on Tao's scattering criteria and Morawetz estimates. This approach provides a more straightforward proof of scattering compared to the traditional concentration-compactness/rigidity method of Kenig and Merle \cite{KENIG}., Comment: 20 pages

We report the first ab initio, non-relativistic QED method that couples light and matter self-consistently beyond the electric dipole approximation and without multipolar truncations. This method is based on an extension of the Maxwell-Pauli-Kohn-Sham approach to a full minimal coupling Hamiltonian, where the space- and time-dependent vector potential is coupled to the matter system, and its back-reaction to the radiated fields is generated by the full current density. The implementation in the open-source Octopus code is designed for massively-parallel multiscale simulations considering different grid spacings for the Maxwell and matter subsystems. Here, we show the first applications of this framework to simulate renormalized Cherenkov radiation of an electronic wavepacket, magnetooptical effects with non-chiral light in non-chiral molecular systems, and renormalized plasmonic modes in a nanoplasmonic dimer. We show that in some cases the beyond-dipole effects can not be captured by a multipolar expansion Hamiltonian in the length gauge. Finally, we discuss further opportunities enabled by the framework in the field of twisted light and orbital angular momentum, inelastic light scattering and strong field physics., Comment: 31 pages, 9 figures, supporting information appended

Mechanical metamaterials are renowned for their ability to achieve high stiffness and strength at low densities, often at the expense of low ductility and stretchability-a persistent trade-off in materials. In contrast, materials such as double-network hydrogels feature interpenetrating compliant and stiff polymer networks, and exhibit unprecedented combinations of high stiffness and stretchability, resulting in exceptional toughness. Here, we present double-network-inspired (DNI) metamaterials by integrating monolithic truss (stiff) and woven (compliant) components into a metamaterial architecture, which achieve a tenfold increase in stiffness and stretchability compared to their pure woven and truss counterparts, respectively. Nonlinear computational mechanics models elucidate that enhanced energy dissipation in these DNI metamaterials stems from increased frictional dissipation due to entanglements between the two networks. Through introduction of internal defects, which typically degrade mechanical properties, we demonstrate an opposite effect of a threefold increase in energy dissipation for these metamaterials via failure delocalization. This work opens avenues for developing new classes of metamaterials in a high-compliance regime inspired by polymer network topologies., Comment: 37 pages, 16 Figures

In this work we explore theoretically whether a parity-violating/chiral light-matter interaction is required to capture all relevant aspects of chiral polaritonics or if a parity-conserving/achiral theory is sufficient (e.g. long-wavelength/dipole approximation). This question is non-trivial to answer, since achiral theories (Hamiltonians) still possess chiral solutions. To elucidate this fundamental theoretical question, a simple GaAs quantum ring model is coupled to an effective chiral mode of a single-handedness optical cavity in dipole approximation. The bare matter GaAs quantum ring possesses a non-degenerate ground state and a doubly degenerate first excited state. The chiral or achiral nature (superpositions) of the degenerate excited state remains undetermined for an isolated matter system. However, inside our parity-conserving description of a chiral cavity, we find that the dressed eigenstates automatically (ab-initio) attain chiral character and become energetically discriminated based on the handedness of the cavity. In contrast, the non-degenerate bare matter state (ground state) does not show an energetic discrimination inside a chiral cavity within dipole approximation. Nevertheless, our results suggest that the handedness of the cavity can still be imprinted onto these states (e.g. angular momentum and chiral current densities). Overall, above findings highlight the relevance of degenerate states in chiral polaritonics. In particularly because recent theoretical results indicate the formation of a frustrated and highly-degenerate electronic ground-state under collective strong coupling conditions, which thus might be prone to chiral symmetry breaking effects.

The incompatibility of explicit diffeomorphism violation with Riemannian geometry within the gravitational Standard-Model Extension (SME) is revisited. We review two methods of how to deal with this problem. The first is based on an approach proposed originally by St\"{u}ckelberg and the latter is to restrict spacetime geometry via the dynamical field equations and the second Bianchi identity. Moreover, a third technique is introduced, which is novel and relies on isometries of a gravitational system. Our conclusion is that an SME background field configuration compatible with Riemannian geometry is more likely to be determined the more diffeomorphisms are isometries of the particular system. This finding has the potential to provide an alternative treatment of explicit spacetime symmetry violation in gravity., Comment: 6 pages, 1 figure

We study a general class of effective backgrounds that break diffeomorphism invariance and their potential roles in cosmology. Specifically, we examine both explicit and spontaneous background fields which display distinct transformation properties and are characterized with different dynamics. For explicit breaking, we focus on the $t$-sector of the minimal gravitational Standard-Model Extension (SME) and for spontaneous breaking on a vector field called the bumblebee model. In both cases, we derive the modified Friedmann equations and find a configuration of the background fields that preserve isotropy and homogeneity. We show that the explicit $t$-sector admits phases of accelerated expansion of the universe with standard matter., Comment: 45 pages and 2 figures

Cancer is a disease that takes millions of lives every year. Then, to propose treatments, avoid recurrence, and improve the patient's life quality, we need to analyze this disease from a biophysical perspective with a solid mathematical formulation. In this paper we introduce a novel deterministic model for the evolution of tumors under several conditions (untreated tumors and treated tumors using chemotherapy). Our model is characterized by a second-order differential equation, whose origin and interpretation are presented by exploiting our understanding of fluid mechanics (via continuity equations) and the theory of differential equations. Additionally, we show that our model can fit various experimental data sets. Thus, we prove that our nuanced and general model can describe accelerated growth, as well as cytostatic and cytotoxic effects. All in all, our model opens up a new window in the understanding of tumor evolution and represents a promising connection between the macroscopic and microscopic descriptions of cancer.

The automatic classification of animal sounds presents an enduring challenge in bioacoustics, owing to the diverse statistical properties of sound signals, variations in recording equipment, and prevalent low Signal-to-Noise Ratio (SNR) conditions. Deep learning models like Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) have excelled in human speech recognition but have not been effectively tailored to the intricate nature of animal sounds, which exhibit substantial diversity even within the same domain. We propose an automated classification framework applicable to general animal sound classification. Our approach first optimizes audio features from Mel-frequency cepstral coefficients (MFCC) including feature rearrangement and feature reduction. It then uses the optimized features for the deep learning model, i.e., an attention-based Bidirectional LSTM (Bi-LSTM), to extract deep semantic features for sound classification. We also contribute an animal sound benchmark dataset encompassing oceanic animals and birds1. Extensive experimentation with real-world datasets demonstrates that our approach consistently outperforms baseline methods by over 25% in precision, recall, and accuracy, promising advancements in animal sound classification.

The pseudo two-color diagram, known as chromosome map (ChM), is a valuable tool for identifying globular clusters (GCs) that consist of single or multiple stellar populations (MPs). Recent surveys of Galactic GCs using the ChM have provided stringent observational constraints on the formation of GCs and their stellar populations. However, these surveys have primarily focused on GCs at moderate distances from the Galactic center and composed of MPs. In this paper, we present the first detailed study of the stellar composition of four GCs in the outer halo of the Milky Way: Arp 2, Ruprecht 106, Terzan 7, and Terzan 8. Our analysis is based on highprecision photometry obtained from images collected with the Hubble Space Telescope in the F275W, F336W, F438W, F606W, and F814W bands. We find that Ruprecht 106 and Terzan 7 are composed solely of a single stellar population, whereas Arp 2 and Terzan 8 host both first- and second-population stars. In these clusters, the second population comprises about half and one-third of the total number of GC stars, respectively. The results from this paper and the literature suggest that the threshold in the initial GC mass, if present, should be smaller than approximately $10^{5}$ $M_{\odot}$. The first-population stars of Arp 2 and Terzan 8, along with the stars of the simple-population GCs Ruprecht 106 and Terzan 7, exhibit intrinsic F275W - F814W color spreads corresponding to [Fe/H] variations of approximately 0.05 - 0.30 dex. This indicates that star-to-star metallicity variations are a common feature of star clusters, regardless of the presence of MPs., Comment: Submitted to ApJ, 17 pages, 7 figures

The scalar sector of the Myers and Pospelov model is considered. This theory introduces a dimension 5 operator with a preferred four-vector which breaks Lorentz symmetry. We investigate various applications using the TFD formalism, a topological field theory that allows the study of thermal and size effects on an equal footing. In this context, Lorentz-violating corrections to the Casimir effect and Stefan-Boltzmann law have been calculated., Comment: 17 pages

We present the first spectroscopic estimates of the chemical abundance of M dwarf stars in a globular cluster (GC), namely 47 Tucanae. By exploiting NIRSpec on board the James Webb Space Telescope (JWST) we gathered low-resolution spectra for 28 stars with masses in the range ~0.4-0.5 solar masses. The spectra are strongly affected by the H2O water vapour bands which can be used as indicators of the oxygen abundance. The spectral analysis reveals that the target stars feature a different O abundance, with a difference of ~0.40 dex between first and the most-polluted second population. The observed range is similar to that observed among red giant stars. This result reinforces previous findings based on the analysis of photometric diagrams, including the ``chromosome maps'', providing a first, and more direct, evidence of light element variations in the M dwarfs' mass regime. The observation that the multiple populations, with their variations in light elements, exhibit the same patterns from the lower main sequence all the way to the red giant branch further strengthens the notion that multiple stellar populations in globular clusters formed in a series of bursts of star formation., Comment: 9 pages, 4 figures, 2 tables, accepted for publication in ApJ Letters

We consider the problem of the reconstruction of a Schwarz matrix from exactly one given eigenvalue. This inverse eigenvalue problem leads to the Jacobi orthogonal polynomials~$\{P_k^{(-n,n)}\}_{k=0}^{n-1}$ that can be treated as a discrete finite analogue of Bessel polynomials.

We consider the focusing inhomogeneous nonlinear Schr\"odinger equation \[ i\partial_t u + \Delta u + |x|^{-b}|u|^\alpha u = 0\qtq{on}\R\times\R^N, \] with $\alpha=\tfrac{4-2b}{N-2}$, $N=\{3,4,5\}$ and $0

Magnesium is one of the important elements in stellar physics as an electron donor and in Galactic Archaeology as a discriminator of different stellar populations. However, previous studies of Mg I and Mg II lines in metal-poor benchmark stars have flagged problems with magnesium abundances inferred from one-dimensional (1D), hydrostatic models of stellar atmospheres, both with or without the local thermodynamic equilibrium (LTE) approximation. We here present 3D non-LTE calculations for magnesium in FG-type dwarfs, and provide corrections for 1D LTE abundances. The 3D non-LTE corrections reduce the ionisation imbalances in the benchmark metal-poor stars HD84937 and HD140283 from $-0.16$ dex and $-0.27$ dex in 1D LTE, to just $-0.02$ dex and $-0.09$ dex respectively. We then applied our abundance corrections to 1D LTE literature results for stars in the thin disc, thick disc, $\alpha$-rich halo, and $\alpha$-poor halo. We find that the 3D non-LTE results show a richer substructure in [Mg/Fe]-[Fe/H] in the $\alpha$-poor halo, revealing two subpopulations at the metal-rich end. These two subpopulations are also separated in kinematics, supporting the astrophysical origin of the separation. While the more magnesium-poor subpopulation is likely to be debris from a massive accreted galaxy, Gaia-Enceladus, the other subpopulation may be related to a previous identified group of stars, called Eos. The presence of additional separation in [Mg/Fe] suggests that previous Mg abundance measurements may have been limited in the precision by the 1D and LTE approximations, highlighting the importance of 3D non-LTE modelling., Comment: accepted to A\&A, 8 pages

Unlike a traditional gyroscope, a visual gyroscope estimates camera rotation through images. The integration of omnidirectional cameras, offering a larger field of view compared to traditional RGB cameras, has proven to yield more accurate and robust results. However, challenges arise in situations that lack features, have substantial noise causing significant errors, and where certain features in the images lack sufficient strength, leading to less precise prediction results. Here, we address these challenges by introducing a novel visual gyroscope, which combines an Efficient Multi-Mask-Filter Rotation Estimator(EMMFRE) and a Learning based optimization(LbTO) to provide a more efficient and accurate rotation estimation from spherical images. Experimental results demonstrate superior performance of the proposed approach in terms of accuracy. The paper emphasizes the advantages of integrating machine learning to optimize analytical solutions, discusses limitations, and suggests directions for future research., Comment: Submitted to 2025 IEEE International Conference on Robotics and Automation (ICRA 2025)

Capturing high resolution imagery of the Earth's surface often calls for a telescope of considerable size, even from Low Earth Orbits (LEO). A large aperture often requires large and expensive platforms. For instance, achieving a resolution of 1m at visible wavelengths from LEO typically requires an aperture diameter of at least 30cm. Additionally, ensuring high revisit times often prompts the use of multiple satellites. In light of these challenges, a small, segmented, deployable CubeSat telescope was recently proposed creating the additional need of phasing the telescope's mirrors. Phasing methods on compact platforms are constrained by the limited volume and power available, excluding solutions that rely on dedicated hardware or demand substantial computational resources. Neural Network (NN) are known for their computationally efficient inference and reduced on board requirements. Therefore we developed a NN based method to measure co phasing errors inherent to a deployable telescope. The proposed technique demonstrates its ability to detect phasing error at the targeted performance level (typically a wavefront error (WFE) below 15 nm RMS for a visible imager operating at the diffraction limit) using a point source. The robustness of the NN method is verified in presence of high order aberrations or noise and the results are compared against existing state of the art techniques. The developed NN model ensures its feasibility and provides a realistic pathway towards achieving diffraction limited images.

The reduction in sea ice cover with Arctic warming facilitates the transit of ships through routes that are remarkably shorter than the traditional shipping routes. Automatic Identification System (AIS), ideally designed to avoid vessel collisions, transmits on vessel navigation information (currently 27 types of messages) such as name, position or speed, is a powerful data source to monitor the progress of Arctic shipping as the ice cover decreases. Based on the analysis of an online platform collecting shipping AIS data, we quantified the spatial distribution of shipping through the Arctic Ocean, its intensity and the temporal evolution, in relation to the area released by the sea ice area. Shipping through the Arctic Ocean is distributed spatially following a heavy-tailed distribution, implying heavy traffic through a limited Arctic area, with an exponent that depends on the vessel category. Fishing is the category with the largest spatial spread, with the width of shipping routes correlated with the proximal sea ice area. The time evolution of these routes is characterized by increasing extended periods of shipping activity through the year. AIS data offers valuable information on the activity of the international fleet worldwide. In the context of the new international agreements, it is a valuable source to monitor shipping, fishing and the potential impact in marine life among other aspects. Here we have focused on the Arctic shipping in recent years, which is rapidly growing, particularly around the Northeastern and Northwest Passage coastal routes, providing an opportunity for the design of shorter shipping routes and reduced greenhouse gas emissions from transport of goods, but at a risk of impacts on the Arctic ecosystem.

We explicitly construct families of simple modules for Lie algebras of rank $2$, on which certain commutative subalgebra acts diagonally and has a simple spectrum. In type $A$ these modules are well known generic Gelfand-Tsetlin modules and they can be viewed as such for other rank $2$ Lie algebras.

Government-imposed lockdowns have challenged academic institutions to transition from traditional face-to-face education into hybrid or fully remote learning models. This transition has focused on the technological challenge of guaranteeing the continuity of sound pedagogy and granting safe access to online digital university services. However, a key requisite involves adapting the evaluation process as well. In response to this need, the authors of this paper tailored and implemented a cloud deployment to provide universal access to online summative assessment of university students in a computer programming course that mirrored a traditional in-person monitored computer laboratory under strictly controlled exam conditions. This deployment proved easy to integrate with the university systems and many commercial proctoring tools. This cloud deployment is not only a solution for extraordinary situations; it can also be adapted daily for online collaborative coding assignments, practical lab sessions, formative assessments, and masterclasses where the students connect using their equipment. Connecting from home facilitates access to education for students with physical disabilities. It also allows participation with their students' own adapted equipment in the evaluation processes, simplifying assessment for those with hearing or visual impairments. In addition to these benefits and the evident commitment to the safety rules, this solution has proven cheaper and more flexible than on-premise equivalent installations., Comment: 14 pages, 8 figures, 1 appendix and 1 code repository

The James Webb Space Telescope (JWST) observations have been demonstrated to be efficient in detecting globular clusters' (GCs) multiple stellar populations in the low mass regime of M dwarfs. We present an overview, and first results, of different projects that can be explored by using the JWST observations gathered under the GO2560 for 47 Tucanae, a first program entirely devoted to the investigation of multiple populations in very low mass stars, which includes spectroscopic data for the faintest GC stars for which spectra are available. Our color-magnitude diagram (CMD) shows some substructures for ultracool stars, including gaps and breaks in slope. In particular, we observe both a gap and a minimum in the F322W2 luminosity function less than one magnitude apart, and discuss which one could be associated with the H-burning limit. We detect stars fainter than this minimum, very likely the brown dwarfs. We corroborate the ubiquity of the multiple populations across different masses, from ~0.1 solar masses up to red giants (~0.8 solar masses). The oxygen range inferred from the M dwarfs, both from the CMD and from the spectra of two M dwarfs associated with different populations, is similar to that observed in giants. We have not detected any difference between the fractions of stars in distinct populations across stellar masses >~0.1 solar masses. This work demonstrates the JWST's capability in uncovering multiple populations within M dwarfs and illustrates the possibility to analyse very low-mass stars in GCs approaching the H-burning limit and the brown-dwarf sequence., Comment: 19 pages, 10 figures, 2 tables, accepted for publication in ApJ

Tele-operated Driving (ToD) is a challenging use case for mobile network operators. Video captured by the built-in vehicle cameras must be streamed meeting a latency requirement of 5 ms with a 99.999% reliability. Although 5G offers high bandwidth, ultra-low latencies and high reliability; ToD service requirements are violated due to bad channel conditions. Ignoring the channel state may lead to over-estimate the number of ToD vehicles that can meet the service requirements, hence comprising the vehicle security. To fill this gap, in this letter we propose TOVAC, an algorithm that guarantees ToD service requirements by taking adequate admission control and routing decisions. This is achieved by using a channel-based capacity graph that determines the maximum number of vehicles that can be tele-operated in any road section. We evaluate TOVAC considering cellular deployments from Turin and show that, unlike a state of the art solution, TOVAC guarantees the ToD service requirements., Comment: 5 pages, 5 figures

Spinodal metamaterials, with architectures inspired by natural phase-separation processes, have presented a significant alternative to periodic and symmetric morphologies when designing mechanical metamaterials with extreme performance. While their elastic mechanical properties have been systematically determined, their large-deformation, nonlinear responses have been challenging to predict and design, in part due to limited data sets and the need for complex nonlinear simulations. This work presents a novel physics-enhanced machine learning (ML) and optimization framework tailored to address the challenges of designing intricate spinodal metamaterials with customized mechanical properties in large-deformation scenarios where computational modeling is restrictive and experimental data is sparse. By utilizing large-deformation experimental data directly, this approach facilitates the inverse design of spinodal structures with precise finite-strain mechanical responses. The framework sheds light on instability-induced pattern formation in spinodal metamaterials -- observed experimentally and in selected nonlinear simulations -- leveraging physics-based inductive biases in the form of nonconvex energetic potentials. Altogether, this combined ML, experimental, and computational effort provides a route for efficient and accurate design of complex spinodal metamaterials for large-deformation scenarios where energy absorption and prediction of nonlinear failure mechanisms is essential.

The amount of Adaptive Optics (AO) telemetry generated by VIS/NIR ground-based observatories is ever greater, leading to a growing need for a standardised data exchange format to support performance analysis and AO research and development activities that involve large-scale telemetry mining, processing, and curation. This paper introduces the Adaptive Optics Telemetry (AOT) data exchange format as a standard for sharing AO telemetry from visible/infrared ground-based observatories. AOT is based on the Flexible Image Transport System (FITS) and aims to provide unambiguous and consistent data access across various systems and configurations, including natural and single/multiple laser guide-star AO systems. We designed AOT focused on two key use cases: atmospheric turbulence parameter estimation and point-spread function reconstruction (PSF-R). We prototyped and tested the design using existing AO telemetry datasets from multiple systems: single conjugate with natural and laser guide stars, tomographic systems with multi-channel wavefront sensors, single and multi wavefront correctors in systems featuring either a Shack-Hartmann or Pyramid as main wavefront sensors. The AOT file structure has been thoroughly defined, specifying data fields, descriptions, data types, units, and expected dimensions. To support this format, we have developed a Python package that enables data conversion, reading, writing and exploration of AOT files, which has been made publicly available and compatible with a general-purpose Python package manager. We demonstrate the flexibility of the AOT format by packaging data from five different instruments, installed on different telescopes.

Metamaterials with functional responses can exhibit varying properties under different conditions (e.g., wave-based responses or deformation-induced property variation). This work addresses the rapid inverse design of such metamaterials to meet target qualitative functional behaviors, a challenge due to its intractability and non-unique solutions. Unlike data-intensive and non-interpretable deep-learning-based methods, we propose the Random-forest-based Interpretable Generative Inverse Design (RIGID), a single-shot inverse design method for fast generation of metamaterial designs with on-demand functional behaviors. RIGID leverages the interpretability of a random forest-based "design$\rightarrow$response" forward model, eliminating the need for a more complex "response$\rightarrow$design" inverse model. Based on the likelihood of target satisfaction derived from the trained random forest, one can sample a desired number of design solutions using Markov chain Monte Carlo methods. We validate RIGID on acoustic and optical metamaterial design problems, each with fewer than 250 training samples. Compared to the genetic algorithm-based design generation approach, RIGID generates satisfactory solutions that cover a broader range of the design space, allowing for better consideration of additional figures of merit beyond target satisfaction. This work offers a new perspective on solving on-demand inverse design problems, showcasing the potential for incorporating interpretable machine learning into generative design under small data constraints., Comment: Accepted by Advanced Intelligent Systems