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6. Boundary integrated neural networks (BINNs) for 2D elastostatic and piezoelectric problems: Theory and MATLAB code

Author

Zhang, Peijun, Zhang, Chuanzeng, Gu, Yan, Qu, Wenzhen, and Zhao, Shengdong

Subjects
Computer Science - Computational Engineering, Finance, and Science
Abstract

In this paper, we make the first attempt to apply the boundary integrated neural networks (BINNs) for the numerical solution of two-dimensional (2D) elastostatic and piezoelectric problems. BINNs combine artificial neural networks with the well-established boundary integral equations (BIEs) to effectively solve partial differential equations (PDEs). The BIEs are utilized to map all the unknowns onto the boundary, after which these unknowns are approximated using artificial neural networks and resolved via a training process. In contrast to traditional neural network-based methods, the current BINNs offer several distinct advantages. First, by embedding BIEs into the learning procedure, BINNs only need to discretize the boundary of the solution domain, which can lead to a faster and more stable learning process (only the boundary conditions need to be fitted during the training). Second, the differential operator with respect to the PDEs is substituted by an integral operator, which effectively eliminates the need for additional differentiation of the neural networks (high-order derivatives of neural networks may lead to instability in learning). Third, the loss function of the BINNs only contains the residuals of the BIEs, as all the boundary conditions have been inherently incorporated within the formulation. Therefore, there is no necessity for employing any weighing functions, which are commonly used in traditional methods to balance the gradients among different objective functions. Moreover, BINNs possess the ability to tackle PDEs in unbounded domains since the integral representation remains valid for both bounded and unbounded domains. Extensive numerical experiments show that BINNs are much easier to train and usually give more accurate learning solutions as compared to traditional neural network-based methods.

Published
2023

9. Enriched physics-informed neural networks for in-plane crack problems: Theory and MATLAB codes

Author

Gu, Yan, Zhang, Chuanzeng, Zhang, Peijun, and Golub, Mikhail V.

Subjects
Computer Science - Computational Engineering, Finance, and Science, Mathematics - Numerical Analysis, 35M32
Abstract

In this paper, a method based on the physics-informed neural networks (PINNs) is presented to model in-plane crack problems in the linear elastic fracture mechanics. Instead of forming a mesh, the PINNs is meshless and can be trained on batches of randomly sampled collocation points. In order to capture the theoretical singular behavior of the near-tip stress and strain fields, the standard PINNs formulation is enriched here by including the crack-tip asymptotic functions such that the singular solutions at the crack-tip region can be modeled accurately without a high degree of nodal refinement. The learnable parameters of the enriched PINNs are trained to satisfy the governing equations of the cracked body and the corresponding boundary conditions. It was found that the incorporation of the crack-tip enrichment functions in PINNs is substantially simpler and more trouble-free than in the finite element (FEM) or boundary element (BEM) methods. The present algorithm is tested on a class of representative benchmarks with different modes of loading types. Results show that the present method allows the calculation of accurate stress intensity factors (SIFs) with far fewer degrees of freedom. A self-contained MATLAB code and data-sets accompanying this manuscript are also provided., Comment: 31 pages, 17 figures, 5 tables

Published
2022
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14. Omicron infection following vaccination enhances a broad spectrum of immune responses dependent on infection history

Author

Hornsby, Hailey, Nicols, Alexander R., Longet, Stephanie, Liu, Chang, Tomic, Adriana, Angyal, Adrienn, Kronsteiner, Barbara, Tyerman, Jessica K., Tipton, Tom, Zhang, Peijun, Gallis, Marta, Supasa, Piyada, Selvaraj, Muneeswaran, Abraham, Priyanka, Neale, Isabel, Ali, Mohammad, Barratt, Natalie A., Nell, Jeremy M., Gustafsson, Lotta, Strickland, Scarlett, Grouneva, Irina, Rostron, Timothy, Moore, Shona C., Hering, Luisa M., Dobson, Susan L., Bibi, Sagida, Mongkolsapaya, Juthathip, Lambe, Teresa, Wootton, Dan, Hall, Victoria, Hopkins, Susan, Dong, Tao, Barnes, Eleanor, Screaton, Gavin, Richter, Alex, Turtle, Lance, Rowland-Jones, Sarah L., Carroll, Miles, Duncan, Christopher J. A., Klenerman, Paul, Dunachie, Susanna J., Payne, Rebecca P., and de Silva, Thushan I.

Published
2023
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38. Investigation of hospital discharge cases and SARS-CoV-2 introduction into Lothian care homes

Author

Robson, Samuel C., Connor, Thomas R., Loman, Nicholas J., Golubchik, Tanya, Martinez Nunez, Rocio T., Bonsall, David, Rambaut, Andrew, Snell, Luke B., Livett, Rich, Ludden, Catherine, Corden, Sally, Nastouli, Eleni, Nebbia, Gaia, Johnston, Ian, Prieto, Jacqui A., Saeed, Kordo, Jackson, David K., Houlihan, Catherine, Frampton, Dan, Hamilton, William L., Witney, Adam A., Bucca, Giselda, Pope, Cassie F., Moore, Catherine, Thomson, Emma C., Cutino-Moguel, Teresa, Harrison, Ewan M., Smith, Colin P., Rogan, Fiona, Beckwith, Shaun M., Murray, Abigail, Singleton, Dawn, Eastick, Kirstine, Sheridan, Liz A., Randell, Paul, Jackson, Leigh M., Ariani, Cristina V., Gonçalves, Sónia, Fairley, Derek J., Loose, Matthew W., Watkins, Joanne, Moses, Samuel, Nicholls, Sam, Bull, Matthew, Amato, Roberto, Smith, Darren L., Aanensen, David M., Barrett, Jeffrey C., Kele, Beatrix, Aggarwal, Dinesh, Shepherd, James G., Curran, Martin D., Parmar, Surendra, Parker, Matthew D., Williams, Catryn, Glaysher, Sharon, Underwood, Anthony P., Bashton, Matthew, Pacchiarini, Nicole, Loveson, Katie F., Byott, Matthew, Carabelli, Alessandro M., Templeton, Kate E., Peacock, Sharon J., de Silva, Thushan I., Wang, Dennis, Langford, Cordelia F., Sillitoe, John, Gunson, Rory N., Cottrell, Simon, O’Grady, Justin, Kwiatkowski, Dominic, Lillie, Patrick J., Cortes, Nicholas, Moore, Nathan, Thomas, Claire, Burns, Phillipa J., Mahungu, Tabitha W., Liggett, Steven, Beckett, Angela H., Holden, Matthew TG., Levett, Lisa J., Osman, Husam, Hassan-Ibrahim, Mohammed O., Simpson, David A., Chand, Meera, Gupta, Ravi K., Darby, Alistair C., Paterson, Steve, Pybus, Oliver G., Volz, Erik M., de Angelis, Daniela, Robertson, David L., Page, Andrew J., Martincorena, Inigo, Aigrain, Louise, Bassett, Andrew R., Wong, Nick, Taha, Yusri, Erkiert, Michelle J., Spencer Chapman, Michael H., Dewar, Rebecca, McHugh, Martin P., Mookerjee, Siddharth, Aplin, Stephen, Harvey, Matthew, Sass, Thea, Umpleby, Helen, Wheeler, Helen, McKenna, James P., Warne, Ben, Taylor, Joshua F., Chaudhry, Yasmin, Izuagbe, Rhys, Jahun, Aminu S., Young, Gregory R., McMurray, Claire, McCann, Clare M., Nelson, Andrew, Elliott, Scott, Lowe, Hannah, Price, Anna, Crown, Matthew R., Rey, Sara, Roy, Sunando, Temperton, Ben, Shaaban, Sharif, Hesketh, Andrew R., Laing, Kenneth G., Monahan, Irene M., Heaney, Judith, Pelosi, Emanuela, Silviera, Siona, Wilson-Davies, Eleri, Fryer, Helen, Adams, Helen, du Plessis, Louis, Johnson, Rob, Harvey, William T., Hughes, Joseph, Orton, Richard J., Spurgin, Lewis G., Bourgeois, Yann, Ruis, Chris, O'Toole, Áine, Gourtovaia, Marina, Sanderson, Theo, Fraser, Christophe, Edgeworth, Jonathan, Breuer, Judith, Michell, Stephen L., Todd, John A., John, Michaela, Buck, David, Gajee, Kavitha, Kay, Gemma L., Heyburn, David, Charalampous, Themoula, Alcolea-Medina, Adela, Kitchman, Katie, McNal, Alan, Pritch, David T., Dervisevic, Samir, Muir, Peter, Robinson, Esther, Vipond, Barry B., Ramadan, Newara A., Jeanes, Christopher, Weldon, Danni, Catalan, Jana, Jones, Neil, da Silva Filipe, Ana, Williams, Chris, Fuchs, Marc, Miskelly, Julia, Jeffries, Aaron R., Oliver, Karen, Park, Naomi R., Ash, Amy, Koshy, Cherian, Barrow, Magdalena, Buchan, Sarah L., Mantzouratou, Anna, Clark, Gemma, Holmes, Christopher W., Campbell, Sharon, Davis, Thomas, Tan, Ngee Keong, Brown, Julianne R., Harris, Kathryn A., Kidd, Stephen P., Grant, Paul R., Xu-McCrae, Li, Cox, Alison, Madona, Pinglawathee, Pond, Marcus, Randell, Paul A., Withell, Karen T., Williams, Cheryl, Graham, Clive, Denton-Smith, Rebecca, Swindells, Emma, Turnbull, Robyn, Sloan, Tim J., Bosworth, Andrew, Hutchings, Stephanie, Pymont, Hannah M., Casey, Anna, Ratcliffe, Liz, Jones, Christopher R., Knight, Bridget A., Haque, Tanzina, Hart, Jennifer, Irish-Tavares, Dianne, Witele, Eric, Mower, Craig, Watson DipHE, Louisa K., Collins, Jennifer, Eltringham, Gary, Crudgington, Dorian, Macklin, Ben, Iturriza-Gomara, Miren, Lucaci, Anita O., McClure, Patrick C., Carlile, Matthew, Holmes, Nadine, Moore, Christopher, Storey, Nathaniel, Rooke, Stefan, Yebra, Gonzalo, Craine, Noel, Perry, Malorie, Alikhan, Nabil-Fareed, Bridgett, Stephen, Cook, Kate F., Fearn, Christopher, Goudarzi, Salman, Lyons, Ronan A., Williams, Thomas, Haldenby, Sam T., Durham, Jillian, Leonard, Steven, Davies, Robert M., Batra, Rahul, Blane, Beth, Spyer, Moira J., Smith, Perminder, Yavus, Mehmet, Williams, Rachel J., Mahanama, Adhyana IK., Samaraweera, Buddhini, Girgis, Sophia T., Hansford, Samantha E., Green, Angie, Beaver, Charlotte, Bellis, Katherine L., Dorman, Matthew J., Kay, Sally, Prestwood, Liam, Rajatileka, Shavanthi, Quick, Joshua, Poplawski, Radoslaw, Reynolds, Nicola, Mack, Andrew, Morriss, Arthur, Whalley, Thomas, Patel, Bindi, Georgana, Iliana, Hosmillo, Myra, Pinckert, Malte L., Stockton, Joanne, Henderson, John H., Hollis, Amy, Stanley, William, Yew, Wen C., Myers, Richard, Thornton, Alicia, Adams, Alexander, Annett, Tara, Asad, Hibo, Birchley, Alec, Coombes, Jason, Evans, Johnathan M., Fina, Laia, Gatica-Wilcox, Bree, Gilbert, Lauren, Graham, Lee, Hey, Jessica, Hilvers, Ember, Jones, Sophie, Jones, Hannah, Kumziene-Summerhayes, Sara, McKerr, Caoimhe, Powell, Jessica, Pugh, Georgia, Taylor, Sarah, Trotter, Alexander J., Williams, Charlotte A., Kermack, Leanne M., Foulkes, Benjamin H., Gallis, Marta, Hornsby, Hailey R., Louka, Stavroula F., Pohare, Manoj, Wolverson, Paige, Zhang, Peijun, MacIntyre-Cockett, George, Trebes, Amy, Moll, Robin J., Ferguson, Lynne, Goldstein, Emily J., Maclean, Alasdair, Tomb, Rachael, Starinskij, Igor, Thomson, Laura, Southgate, Joel, Kraemer, Moritz UG., Raghwani, Jayna, Zarebski, Alex E., Boyd, Olivia, Geidelberg, Lily, Illingworth, Chris J., Jackson, Chris, Pascall, David, Vattipally, Sreenu, Freeman, Timothy M., Hsu, Sharon N., Lindsey, Benjamin B., James, Keith, Lewis, Kevin, Tonkin-Hill, Gerry, Tovar-Corona, Jaime M., Cox, MacGregor, Abudahab, Khalil, Menegazzo, Mirko, Taylor, Ben EW., Yeats, Corin A., Mukaddas, Afrida, Wright, Derek W., de Oliveira Martins, Leonardo, Colquhoun, Rachel, Hill, Verity, Jackson, Ben, McCrone, J.T., Medd, Nathan, Scher, Emily, Keatley, Jon-Paul, Curran, Tanya, Morgan, Sian, Maxwell, Patrick, Smith, Ken, Eldirdiri, Sahar, Kenyon, Anita, Holmes, Alison H., Price, James R., Wyatt, Tim, Mather, Alison E., Skvortsov, Timofey, Hartley, John A., Guest, Martyn, Kitchen, Christine, Merrick, Ian, Munn, Robert, Bertolusso, Beatrice, Lynch, Jessica, Vernet, Gabrielle, Kirk, Stuart, Wastnedge, Elizabeth, Stanley, Rachael, Idle, Giles, Bradley, Declan T., Killough, Nicholas F., Poyner, Jennifer, Mori, Matilde, Jones, Owen, Wright, Victoria, Brooks, Ellena, Churcher, Carol M., Delgado Callico, Laia, Fragakis, Mireille, Galai, Katerina, Jermy, Andrew, Judges, Sarah, Markov, Anna, McManus, Georgina M., Smith, Kim S., Thomas-McEwen, Peter MD., Westwick, Elaine, Attwood, Stephen W., Bolt, Frances, Davies, Alisha, De Lacy, Elen, Downing, Fatima, Edwards, Sue, Meadows, Lizzie, Jeremiah, Sarah, Smith, Nikki, Foulser, Luke, Patel, Amita, Berry, Louise, Boswell, Tim, Fleming, Vicki M., Howson-Wells, Hannah C., Joseph, Amelia, Khakh, Manjinder, Lister, Michelle M., Bird, Paul W., Fallon, Karlie, Helmer, Thomas, McMurray, Claire L., Odedra, Mina, Shaw, Jessica, Tang, Julian W., Willford, Nicholas J., Blakey, Victoria, Raviprakash, Veena, Sheriff, Nicola, Williams, Lesley-Anne, Feltwell, Theresa, Bedford, Luke, Cargill, James S., Hughes, Warwick, Moore, Jonathan, Stonehouse, Susanne, Atkinson, Laura, Lee, Jack CD., Shah, Divya, Ohemeng-Kumi, Natasha, Ramble, John, Sehmi, Jasveen, Williams, Rebecca, Chatterton, Wendy, Pusok, Monika, Everson, William, Castigador, Anibolina, Macnaughton, Emily, El Bouzidi, Kate, Lampejo, Temi, Sudhanva, Malur, Breen, Cassie, Sluga, Graciela, Ahmad, Shazaad SY., George, Ryan P., Machin, Nicholas W., Binns, Debbie, James, Victoria, Blacow, Rachel, Coupland, Lindsay, Smith, Louise, Barton, Edward, Padgett, Debra, Scott, Garren, Cross, Aidan, Mirfenderesky, Mariyam, Greenaway, Jane, Cole, Kevin, Clarke, Phillip, Duckworth, Nichola, Walsh, Sarah, Bicknell, Kelly, Impey, Robert, Wyllie, Sarah, Hopes, Richard, Bishop, Chloe, Chalker, Vicki, Harrison, Ian, Gifford, Laura, Molnar, Zoltan, Auckland, Cressida, Evans, Cariad, Johnson, Kate, Partridge, David G., Raza, Mohammad, Baker, Paul, Bonner, Stephen, Essex, Sarah, Murray, Leanne J., Lawton, Andrew I., Burton-Fanning, Shirelle, Payne, Brendan AI., Waugh, Sheila, Gomes, Andrea N., Kimuli, Maimuna, Murray, Darren R., Ashfield, Paula, Dobie, Donald, Ashford, Fiona, Best, Angus, Crawford, Liam, Cumley, Nicola, Mayhew, Megan, Megram, Oliver, Mirza, Jeremy, Moles-Garcia, Emma, Percival, Benita, Driscoll, Megan, Ensell, Leah, Lowe, Helen L., Maftei, Laurentiu, Mondani, Matteo, Chaloner, Nicola J., Cogger, Benjamin J., Easton, Lisa J., Huckson, Hannah, Lewis, Jonathan, Lowdon, Sarah, Malone, Cassandra S., Munemo, Florence, Mutingwende, Manasa, Nicodemi, Roberto, Podplomyk FD, Olga, Somassa, Thomas, Beggs, Andrew, Richter, Alex, Cormie, Claire, Dias, Joana, Forrest, Sally, Higginson, Ellen E., Maes, Mailis, Young, Jamie, Davidson, Rose K., Jackson, Kathryn A., Keeley, Alexander J., Ball, Jonathan, Byaruhanga, Timothy, Chappell, Joseph G., Dey, Jayasree, Hill, Jack D., Park, Emily J., Fanaie, Arezou, Hilson, Rachel A., Yaze, Geraldine, Lo, Stephanie, Afifi, Safiah, Beer, Robert, Maksimovic, Joshua, McCluggage, Kathryn, Spellman, Karla, Bresner, Catherine, Fuller, William, Marchbank, Angela, Workma, Trudy, Shelest, Ekaterina, Debebe, Johnny, Sang, Fei, Francois, Sarah, Gutierrez, Bernardo, Vasylyeva, Tetyana I., Flaviani, Flavia, Ragonnet-Cronin, Manon, Smollett, Katherine L., Broos, Alice, Mair, Daniel, Nichols, Jenna, Nomikou, Kyriaki, Tong, Lily, Tsatsani, Ioulia, O'Brien, Sarah, Rushton, Steven, Sanderson, Roy, Perkins, Jon, Cotton, Seb, Gallagher, Abbie, Allara, Elias, Pearson, Clare, Bibby, David, Dabrer, Gavin, Ellaby, Nicholas, Gallagher, Eileen, Hubb, Jonathan, Lackenby, Angie, Lee, David, Manesis, Nikos, Mbisa, Tamyo, Platt, Steven, Twohig, Katherine A., Morgan, Mari, Aydin, Alp, Baker, David J., Foster-Nyarko, Ebenezer, Prosolek, Sophie J., Rudder, Steven, Baxter, Chris, Carvalho, Sílvia F., Lavin, Deborah, Mariappan, Arun, Radulescu, Clara, Singh, Aditi, Tang, Miao, Morcrette, Helen, Bayzid, Nadua, Cotic, Marius, Balcazar, Carlos E., Gallagher, Michael D., Maloney, Daniel, Stanton, Thomas D., Williamson, Kathleen A., Manley, Robin, Michelsen, Michelle L., Sambles, Christine M., Studholme, David J., Warwick-Dugdale, Joanna, Eccles, Richard, Gemmell, Matthew, Gregory, Richard, Hughes, Margaret, Nelson, Charlotte, Rainbow, Lucille, Vamos, Edith E., Webster, Hermione J., Whitehead, Mark, Wierzbicki, Claudia, Angyal, Adrienn, Green, Luke R., Whiteley, Max, Betteridge, Emma, Bronner, Iraad F., Farr, Ben W., Goodwin, Scott, Lensing, Stefanie V., McCarthy, Shane A., Quail, Michael A., Rajan, Diana, Redshaw, Nicholas M., Scott, Carol, Shirley, Lesley, Thurston, Scott AJ., Rowe, Will, Gaskin, Amy, Le-Viet, Thanh, Bonfield, James, Liddle, Jennifier, Whitwham, Andrew, Cotton, S., McHugh, M.P., Dewar, R., Haas, J.G., and Templeton, K.

Published
2023
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45. Comparative genomics provides insights into the aquatic adaptations of mammals

Author

Yuan, Yuan, Zhang, Yaolei, Zhang, Peijun, Liu, Chang, Wang, Jiahao, Gao, Haiyu, Hoelzel, A. Rus, Seim, Inge, Lv, Meiqi, Lin, Mingli, Dong, Lijun, Gao, Haoyang, Yang, Zixin, Caruso, Francesco, Lin, Wenzhi, da Fonseca, Rute R., Wang, Ding, Wang, Xianyan, Rasmussen, Marianne H., Liu, Mingming, Zheng, Jinsong, Zhao, Liyuan, Campos, Paula F., Kang, Hui, Iversen, Maria, Song, Yue, Guo, Xinyu, Guo, Jiao, Qin, Yating, Pan, Shanshan, Xu, Qiwu, Meng, Lingfeng, A, Yunga, Liu, Shanshan, Lee, Simon Ming-Yuen, Liu, Xin, Xu, Xun, Yang, Huanming, Fan, Guangyi, Wang, Kun, and Li, Songhai

Published
2021

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