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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2107.00940">arXiv:2107.00940</a> <span> [<a href="https://arxiv.org/pdf/2107.00940">pdf</a>, <a href="https://arxiv.org/ps/2107.00940">ps</a>, <a href="https://arxiv.org/format/2107.00940">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computational Physics">physics.comp-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantitative Methods">q-bio.QM</span> </div> </div> <p class="title is-5 mathjax"> Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&query=Maddu%2C+S">Suryanarayana Maddu</a>, <a href="/search/physics?searchtype=author&query=Sturm%2C+D">Dominik Sturm</a>, <a href="/search/physics?searchtype=author&query=M%7F%C3%BCller%2C+C+L">Christian L. M眉ller</a>, <a href="/search/physics?searchtype=author&query=Sbalzarini%2C+I+F">Ivo F. Sbalzarini</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2107.00940v1-abstract-short" style="display: inline;"> We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as Physics Informed Neural Networks (PINNs). PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. Their training amounts to solving an optimization problem over a weighted sum of dat… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.00940v1-abstract-full').style.display = 'inline'; document.getElementById('2107.00940v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2107.00940v1-abstract-full" style="display: none;"> We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as Physics Informed Neural Networks (PINNs). PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. Their training amounts to solving an optimization problem over a weighted sum of data-fidelity and equation-fidelity objectives. Conflicts between objectives can arise from scale imbalances, heteroscedasticity in the data, stiffness of the physical equation, or from catastrophic interference during sequential training. We explain the training pathology arising from this and propose a simple yet effective inverse-Dirichlet weighting strategy to alleviate the issue. We compare with Sobolev training of neural networks, providing the baseline of analytically $\boldsymbol蔚$-optimal training. We demonstrate the effectiveness of inverse-Dirichlet weighting in various applications, including a multi-scale model of active turbulence, where we show orders of magnitude improvement in accuracy and convergence over conventional PINN training. For inverse modeling using sequential training, we find that inverse-Dirichlet weighting protects a PINN against catastrophic forgetting. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.00940v1-abstract-full').style.display = 'none'; document.getElementById('2107.00940v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1402.6135">arXiv:1402.6135</a> <span> [<a href="https://arxiv.org/pdf/1402.6135">pdf</a>, <a href="https://arxiv.org/format/1402.6135">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1107/S1600577514006857">10.1107/S1600577514006857 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Characterization of Spatial Coherence of Synchrotron Radiation with Non-Redundant Arrays of Apertures </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/physics?searchtype=author&query=Skopintsev%2C+P">P. Skopintsev</a>, <a href="/search/physics?searchtype=author&query=Singer%2C+A">A. Singer</a>, <a href="/search/physics?searchtype=author&query=Bach%2C+J">J. Bach</a>, <a href="/search/physics?searchtype=author&query=M%7Fuller%2C+L">L. Muller</a>, <a href="/search/physics?searchtype=author&query=Beyersdorf%2C+B">B. Beyersdorf</a>, <a href="/search/physics?searchtype=author&query=Schleitzer%2C+S">S. Schleitzer</a>, <a href="/search/physics?searchtype=author&query=Gorobtsov%2C+O">O. Gorobtsov</a>, <a href="/search/physics?searchtype=author&query=Shabalin%2C+A">A. Shabalin</a>, <a href="/search/physics?searchtype=author&query=Kurta%2C+R">R. Kurta</a>, <a href="/search/physics?searchtype=author&query=Dzhigaev%2C+D">D. Dzhigaev</a>, <a href="/search/physics?searchtype=author&query=Yefanov%2C+O+M">O. M. Yefanov</a>, <a href="/search/physics?searchtype=author&query=Glaser%2C+L">L. Glaser</a>, <a href="/search/physics?searchtype=author&query=Sakdinawat%2C+A">A. Sakdinawat</a>, <a href="/search/physics?searchtype=author&query=Liu%2C+Y">Y. Liu</a>, <a href="/search/physics?searchtype=author&query=Gr%7Fubel%2C+G">G. Grubel</a>, <a href="/search/physics?searchtype=author&query=Fr%7Fomter%2C+R">R. Fromter</a>, <a href="/search/physics?searchtype=author&query=Oepen%2C+H+P">H. P. Oepen</a>, <a href="/search/physics?searchtype=author&query=Viefhaus%2C+J">J. Viefhaus</a>, <a href="/search/physics?searchtype=author&query=Vartanyants%2C+I+A">I. A. Vartanyants</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1402.6135v1-abstract-short" style="display: inline;"> We present a method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern. The technique is based on scattering from non-redundant arrays (NRA) of slits and records the degree of spatial coherence at several relative separations from one to 15 microns, simultaneously. Using NRAs we measured the transverse coherence of the X-ray beam at the XUV X-ray beamli… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.6135v1-abstract-full').style.display = 'inline'; document.getElementById('1402.6135v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1402.6135v1-abstract-full" style="display: none;"> We present a method to characterize the spatial coherence of soft X-ray radiation from a single diffraction pattern. The technique is based on scattering from non-redundant arrays (NRA) of slits and records the degree of spatial coherence at several relative separations from one to 15 microns, simultaneously. Using NRAs we measured the transverse coherence of the X-ray beam at the XUV X-ray beamline P04 of the PETRA III synchrotron storage ring as a function of different beam parameters. To verify the results obtained with the NRAs additional Young's double pinhole experiments were conducted and show good agreement. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1402.6135v1-abstract-full').style.display = 'none'; document.getElementById('1402.6135v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 February, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 6 figures, 2 tables, 42 references</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Synchrotron Rad. 21 Part 4, pages 722-728. 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