Convergence and error analysis of PINNs

Physics-informed neural networks (PINNs) are a promising approach that combines the power of neural networks with the interpretability of physical modeling. PINNs have shown good practical performance in solving partial differential equations (PDEs) and in hybrid modeling scenarios, where physical models enhance data-driven approaches. However, it is essential to establish their theoretical properties in order to fully understand their capabilities and limitations. In this study, we highlight that classical training of PINNs can suffer from systematic overfitting. This problem can be addressed by adding a ridge regularization to the empirical risk, which ensures that the resulting estimator is risk-consistent for both linear and nonlinear PDE systems. However, the strong convergence of PINNs to a solution satisfying the physical constraints requires a more involved analysis using tools from functional analysis and calculus of variations. In particular, for linear PDE systems, an implementable Sobolev-type regularization allows to reconstruct a solution that not only achieves statistical accuracy but also maintains consistency with the underlying physics

SU(4) symmetry breaking revealed by magneto-optical spectroscopy in epitaxial graphene

Refined infrared magnetotransmission experiments have been performed in magnetic fields B up to 35 T on a series of multilayer epitaxial graphene samples. Following the main optical transition involving the n=0 Landau level (LL), we observe a new absorption transition increasing in intensity with magnetic fields B>26 T. Our analysis shows that this is a signature of the breaking of the SU(4) symmetry of the n=0 LL. Using a quantitative model, we show that the only symmetry-breaking scheme consistent with our experiments is a charge density wave (CDW)

ENTRE SYLVICULTURE ET PATURAGE DANS LES ESPACES BOISES DE LA ZONE MEDITERRANEENNE FRANÇAISE L'INNOVATION SYLVOPASTORALE EN QUESTIONS

N° ISBN - 978-2-7380-1284-5International audienceIn northern Mediterranean regions, livestock farming and silviculture evolutions have them sometimes gathered sometimes separated. The marginalization of little productive and costly to exploit Mediterranean forests and the economic and climatic difficulties faced by livestock sector in these regions calls for a fresh examination of silvopastoralism. In woodlands, fodder production is staggered over the year and its herbaceous component is preserved longer thanks to the shadow of trees. So it makes for example a summer pastoral resource. The selective cutting of trees generates wood products which may be sold, besides conventional outlets such as triturating and firewood, through new marketing channels such as wood energy or construction. Grazing keeps underbrush under control and facilitates later silviculture operations. Reciprocally, silviculture operations increase the quantity of light reaching undergrowth and thereby favours the development of forage resources : grass growth, lower hanging foliage, increase in percent fruit set. They also facilitate animal circulation. The construction of this productive consistency asks several questions, at different scales, which the paper tries to answer offering : (i) a silvopastoral interpretation of wooded environments ; (ii) a characterization of trees partial taking ; (iii) a characterization of wooded areas pastoral uses ; (iv) a different levels of silvopastoral project consistency analysis

Uncertainties in assessing annual nitrate loads and concentration indicators. Part 1: Impact of sampling frequency and load estimation alogorithms

International audienceThe objectives of this study are to evaluate the uncertainty in annual nitrate loads and concentrations (such as annual average and median concentrations) as induced by infrequent sampling and by the algorithms used to compute fluxes. A total of 50 watershed-years of hourly to daily flow and concentration data gathered from nine watersheds (5 to 252 km2) in Brittany, France, were analyzed. Original (high frequency) nitrate concentration and flow data were numerically sampled to simulate common sampling frequencies. Annual fluxes and concentration indicators calculated from the simulated samples were compared to the reference values calculated from the high-frequency data. The uncertainties contributed by several algorithms used to calculate annual fluxes were also quantified. In all cases, uncertainty increased as sampling intervals increased. Results showed that all the tested algorithms that do not use continuous flow data to compute nitrate fluxes introduced considerable uncertainty. The flowƒ]weighted average concentration ratio method was found to perform best across the 50 annual datasets. Analysis of the bias values suggests that the 90th and 95th percentiles and the maximum concentration values tend to be systematically underestimated in the long term, but the load estimates (using the chosen algorithm) and the average and median concentrations were relatively unbiased. Great variability in the precision of the load estimation algorithms was observed, both between watersheds of different sizes and between years for a particular watershed. This has prevented definitive uncertainty predictions for nitrate loads and concentrations in this preliminary work, but suggests that hydrologic factors, such as the watershed hydrological reactivity, could be a key factor in predicting uncertainty levels

Télédétection de la trame verte arborée en haute résolution par morphologie mathématique

International audienceCet article pointe d'abord les causes et/es enjeux des verrous cartographiques dans !a mise en oeuvre de la politique de la trame verte et bleue (TVB). Une connaissance de l'emprise précise de la trame verte arborée par les acteurs locaux apparaît incontournable. Nous proposons ensuite une méthode de télédétection associée à des algorithmes de morphologie mathématique pour extraire la trame verte arborée à l'échelle métrique à partir d'une image à très haute résolution spatiale. La méthode proposée est une séquence de quatre étapes : 1) analyse en composantes principales (ACP), 2) segmentation par la transformation chapeau haut de forme, 3) élimination du bruit morphologique, 4) restauration des contours arborés par dilatation géodésique. Enfin, une discussion sur les perspectives en termes de conséquences sur les méthodologies de télédétection et sur les politiques publiques environnementales termine l'article

Le lait de vache dans l'alimentation du nourrisson, avantages et inconvénients

L alimentation du nourrisson est fondamentale pour son développement physique mais également sa maturation cérébrale à court et plus long terme. Le lait maternel constitue l aliment le plus adapté à la croissance du nouveau-né. En France, le taux d allaitement, avoisinant les 60%, est le plus bas d Europe. Des initiatives sont cependant mises en place afin de valoriser ce mode d alimentation auprès des familles, des autorités et des professionnels de santé. Les alternatives à l allaitement maternel sont les formules lactées infantiles au lait de vache. Ce lait, pleinement adapté à la croissance du veau s avère trop riche pour un nouveau-né. Comment est-il transformé pour apporter les éléments essentiels à la croissance de l enfant ? Suite aux avancées de la recherche et de l industrie du lait, la gamme des préparations infantiles s est diversifiée, proposant ainsi des produits de plus en plus adaptées aux différentes situations. L utilisation de ces formules provoque cependant chez certains nourrissons deux types de pathologies : l allergie aux protéines de lait de vache et l intolérance au lactose. Premier professionnel de santé consulté par les nouveaux parents, le pharmacien d officine se doit d apporter des conseils appropriés, de rassurer et de réorienter ces derniers lors de pathologies particulières ou de choix de matériel pour leur enfant.Infant nutrition is essential for both physical development and brain maturation in short and medium term. Breast milk is the most suitable food for the growth of newborn. In France, the feeding rate is about 60 %, the lowest in Europe. However, some initiatives have been set up in order to enhance this feeding way with some authorities, families and healthcare professionals. Cow s milk formulas are an alternative to breastfeeding. This milk, totally adapted to the growth of calf is too rich for newborn. How is it processed to provide what children need? Thanks to research programs and dairy industry investments, the range of infant formulas has been diversified, offering products adapted to many situations. However, using these formulas causes in some children two diseases: cow' s milk protein allergy and lactose intolerance. As the first healthcare professional consulted by the new parents, the pharmacist has to provide appropriate advices, reassure and redirect them in case of childhood disease. He should also be able to advise parents in choosing appropriate equipment for their baby.ANGERS-BU Médecine-Pharmacie (490072105) / SudocSudocFranceF