Fitting model to intensity plot

I am trying to fit a model to the following dataset to extract numerical values for 4 parameters $ J_x$ , $ J_y$ , $ J_z$ , and $ g$ . I also know that $ g \approx 2$ in this case. The dataset is a list of quadruples: {x, energy, intensity, error} as shown below

dataset = {{0.01299648, 0.01203211, 0.1263361, 0.005950636}, {0.01299648, 0.04910681, 0.0336076, 0.002947696}, {0.01299648, 0.09977061, 0.001322289, 0.000413821}, {0.01299648, 0.1508783, 0.000499663, 0.000258259}, {0.01299648, 0.2008796, 0.000419055, 0.00024877}, {0.01299648, 0.2510364, 0.000421737, 0.000272571}, {0.01299648, 0.3009251, 0.000178943, 0.000156955}, {0.01299648, 0.3508747, 0.0000992, 0.0000883}, {0.01299648, 0.3999321, 0.000430162, 0.000468312}, {0.01299648, 0.4489179, 0.001252234, 0.000846992}, {0.01299648, 0.5002585, 0.000617269, 0.000553035}, {0.01299648, 0.5509165, 0.001468457, 0.000842178}, {0.01299648, 0.6011173, 0.003723728, 0.001349723}, {0.01299648, 0.6498302, 0.004062989, 0.001265983}, {0.01299648, 0.6988636, 0.001993023, 0.000906512}, {0.01299648, 0.7499531, 0.000721637, 0.000587884}, {0.01299648, 0.8010127, 0.000252952, 0.000316284}, {0.05334629, 0.01203211, 0.1305249, 0.004184997}, {0.05334629, 0.04910681, 0.03503799, 0.002187056}, {0.05334629, 0.09977061, 0.001494748, 0.000322744}, {0.05334629, 0.1508783, 0.000631434, 0.000216124}, {0.05334629, 0.2008796, 0.000516482, 0.000212526}, {0.05334629, 0.2510364, 0.000452927, 0.000203133}, {0.05334629, 0.3009251, 0.00038714, 0.000173926}, {0.05334629, 0.3508747, 0.000419254, 0.000179236}, {0.05334629, 0.3999321, 0.000425151, 0.000310161}, {0.05334629, 0.4489179, 0.000511058, 0.000412408}, {0.05334629, 0.5002585, 0.000683154, 0.000400352}, {0.05334629, 0.5509165, 0.001937698, 0.000617178}, {0.05334629, 0.6011173, 0.003902016, 0.000892543}, {0.05334629, 0.6498302, 0.00309874, 0.000839511}, {0.05334629, 0.6988636, 0.001156821, 0.000561058}, {0.05334629, 0.7499531, 0.000876003, 0.000445513}, {0.05334629, 0.8010127, 0.000494271, 0.000353135}, {0.05334629, 0.8507249, 0.000468474, 0.000405826}, {0.05334629, 0.9009042, 0.000227273, 0.000284132}, {0.09946869, 0.01203211, 0.1314684, 0.002607759}, {0.09946869, 0.04910681, 0.03540794, 0.001393436}, {0.09946869, 0.09977061, 0.001480958, 0.000215194}, {0.09946869, 0.1508783, 0.000518701, 0.000144396}, {0.09946869, 0.2008796, 0.00039427, 0.000139293}, {0.09946869, 0.2510364, 0.000395253, 0.000148412}, {0.09946869, 0.3009251, 0.000357242, 0.000144663}, {0.09946869, 0.3508747, 0.000435539, 0.000173756}, {0.09946869, 0.3999321, 0.000440639, 0.000186949}, {0.09946869, 0.4489179, 0.000453975, 0.000189049}, {0.09946869, 0.5002585, 0.000817151, 0.000265822}, {0.09946869, 0.5509165, 0.002821699, 0.000522746}, {0.09946869, 0.6011173, 0.005799377, 0.000790837}, {0.09946869, 0.6498302, 0.003142505, 0.000619193}, {0.09946869, 0.6988636, 0.00089875, 0.000377157}, {0.09946869, 0.7499531, 0.000935933, 0.000440654}, {0.09946869, 0.8010127, 0.000741281, 0.00040915}, {0.09946869, 0.8507249, 0.000379727, 0.000311241}, {0.09946869, 0.9009042, 0.000452129, 0.000372186}, {0.09946869, 0.9499643, 0.000321497, 0.000298012}, {0.09946869, 0.9987899, 0.000216047, 0.000265462}, {0.09946869, 1.049146, 0.000321083, 0.000405456}, {0.09946869, 1.100007, 0.00007, 0.000197968}, {0.09946869, 1.151003, 0.000371132, 0.000898138}, {0.09946869, 1.20088, 0.001603127, 0.001909191}, {0.1513923, 0.01203211, 0.1271927, 0.002382964}, {0.1513923, 0.04910681, 0.03466543, 0.001207942}, {0.1513923, 0.09977061, 0.001471831, 0.000180972}, {0.1513923, 0.1508783, 0.000458085, 0.000108564}, {0.1513923, 0.2008796, 0.000323088, 0.0000968}, {0.1513923, 0.2510364, 0.000262988, 0.0000927}, {0.1513923, 0.3009251, 0.000208331, 0.0000952}, {0.1513923, 0.3508747, 0.000261884, 0.000132211}, {0.1513923, 0.3999321, 0.000318829, 0.000154663}, {0.1513923, 0.4489179, 0.000390393, 0.000170512}, {0.1513923, 0.5002585, 0.000796483, 0.000230864}, {0.1513923, 0.5509165, 0.003169181, 0.00045884}, {0.1513923, 0.6011173, 0.006016299, 0.000634249}, {0.1513923, 0.6498302, 0.002961305, 0.000479318}, {0.1513923, 0.6988636, 0.00089255, 0.00030299}, {0.1513923, 0.7499531, 0.000601942, 0.000292041}, {0.1513923, 0.8010127, 0.000622036, 0.000308231}, {0.1513923, 0.8507249, 0.00059582, 0.000311122}, {0.1513923, 0.9009042, 0.000342461, 0.000258311}, {0.1513923, 0.9499643, 0.000365842, 0.000264302}, {0.1513923, 0.9987899, 0.000383168, 0.000282596}, {0.1513923, 1.049146, 0.000158197, 0.000218464}, {0.1513923, 1.100007, 0.0000797, 0.0001487}, {0.1513923, 1.151003, 0.000272186, 0.000602807}, {0.1513923, 1.20088, 0.000791483, 0.000943182}, {0.1513923, 1.24981, 0.000810134, 0.000846855}, {0.1513923, 1.298876, 0.001098106, 0.000878741}, {0.1513923, 1.35012, 0.001020097, 0.00091243}, {0.1513923, 1.400843, 0.00099628, 0.001472998}, {0.1513923, 1.45113, 0.001696679, 0.002615917}, {0.1513923, 1.487999, 0.00068497, 0.001417412}, {0.200413, 0.01203211, 0.1251366, 0.002421743}, {0.200413, 0.04910681, 0.03396657, 0.001239589}, {0.200413, 0.09977061, 0.001455514, 0.000186787}, {0.200413, 0.1508783, 0.000471295, 0.000107087}, {0.200413, 0.2008796, 0.000356116, 0.0000954}, {0.200413, 0.2510364, 0.000255785, 0.0000834}, {0.200413, 0.3009251, 0.000192659, 0.0000751}, {0.200413, 0.3508747, 0.000195415, 0.000086}, {0.200413, 0.3999321, 0.000212672, 0.0000972}, {0.200413, 0.4489179, 0.000201986, 0.0000998}, {0.200413, 0.5002585, 0.000452148, 0.00014457}, {0.200413, 0.5509165, 0.002283648, 0.000302595}, {0.200413, 0.6011173, 0.005130702, 0.000435712}, {0.200413, 0.6498302, 0.002947664, 0.000341739}, {0.200413, 0.6988636, 0.000885883, 0.00019889}, {0.200413, 0.7499531, 0.000353508, 0.000142375}, {0.200413, 0.8010127, 0.000337989, 0.000159135}, {0.200413, 0.8507249, 0.000294789, 0.00016511}, {0.200413, 0.9009042, 0.000287179, 0.00017037}, {0.200413, 0.9499643, 0.000311635, 0.000194681}, {0.200413, 0.9987899, 0.000207756, 0.000158586}, {0.200413, 1.049146, 0.000158257, 0.00013942}, {0.200413, 1.100007, 0.000190184, 0.000146221}, {0.200413, 1.151003, 0.000213257, 0.000208235}, {0.200413, 1.20088, 0.000336925, 0.000306631}, {0.200413, 1.24981, 0.000487695, 0.000424801}, {0.200413, 1.298876, 0.000638927, 0.000549385}, {0.200413, 1.35012, 0.001054225, 0.000776587}, {0.200413, 1.400843, 0.001720866, 0.001358017}, {0.200413, 1.45113, 0.00200075, 0.001706196}, {0.200413, 1.487999, 0.001241234, 0.001336194}, {0.249747, 0.01203211, 0.1205826, 0.002361229}, {0.249747, 0.04910681, 0.03260196, 0.001191631}, {0.249747, 0.09977061, 0.001261705, 0.000170178}, {0.249747, 0.1508783, 0.000333223, 0.00009}, {0.249747, 0.2008796, 0.000305626, 0.0000888}, {0.249747, 0.2510364, 0.000248531, 0.0000826}, {0.249747, 0.3009251, 0.000227554, 0.0000828}, {0.249747, 0.3508747, 0.000242098, 0.0000856}, {0.249747, 0.3999321, 0.000213059, 0.0000796}, {0.249747, 0.4489179, 0.000171657, 0.0000691}, {0.249747, 0.5002585, 0.000269242, 0.0000875}, {0.249747, 0.5509165, 0.001302021, 0.000202058}, {0.249747, 0.6011173, 0.003488679, 0.000339568}, {0.249747, 0.6498302, 0.003051286, 0.000322039}, {0.249747, 0.6988636, 0.001461859, 0.000227405}, {0.249747, 0.7499531, 0.000595035, 0.000144464}, {0.249747, 0.8010127, 0.000388456, 0.000118404}, {0.249747, 0.8507249, 0.000291368, 0.00010498}, {0.249747, 0.9009042, 0.000241225, 0.000107813}, {0.249747, 0.9499643, 0.000237664, 0.00011481}, {0.249747, 0.9987899, 0.000151976, 0.0000917}, {0.249747, 1.049146, 0.000151201, 0.000093}, {0.249747, 1.100007, 0.000175435, 0.000106715}, {0.249747, 1.151003, 0.000146402, 0.00010687}, {0.249747, 1.20088, 0.000207344, 0.0001413}, {0.249747, 1.24981, 0.000247186, 0.00017871}, {0.249747, 1.298876, 0.000406102, 0.000266496}, {0.249747, 1.35012, 0.000704678, 0.00045794}, {0.249747, 1.400843, 0.000829369, 0.000665319}, {0.249747, 1.45113, 0.000937308, 0.000875315}, {0.249747, 1.487999, 0.001484896, 0.00116244}, {0.2999469, 0.01203211, 0.1134484, 0.002063204}, {0.2999469, 0.04910681, 0.03021775, 0.001057232}, {0.2999469, 0.09977061, 0.00106177, 0.000140285}, {0.2999469, 0.1508783, 0.00030537, 0.0000768}, {0.2999469, 0.2008796, 0.000213005, 0.0000649}, {0.2999469, 0.2510364, 0.000185747, 0.0000657}, {0.2999469, 0.3009251, 0.000164455, 0.000065}, {0.2999469, 0.3508747, 0.000142963, 0.0000636}, {0.2999469, 0.3999321, 0.000130967, 0.0000592}, {0.2999469, 0.4489179, 0.000167198, 0.0000687}, {0.2999469, 0.5002585, 0.000180923, 0.0000726}, {0.2999469, 0.5509165, 0.000541689, 0.000134283}, {0.2999469, 0.6011173, 0.001467756, 0.000226035}, {0.2999469, 0.6498302, 0.00203471, 0.000272955}, {0.2999469, 0.6988636, 0.001823599, 0.000254749}, {0.2999469, 0.7499531, 0.001339045, 0.000208357}, {0.2999469, 0.8010127, 0.0009652, 0.000182255}, {0.2999469, 0.8507249, 0.00046882, 0.000122285}, {0.2999469, 0.9009042, 0.000292738, 0.000102422}, {0.2999469, 0.9499643, 0.000180685, 0.0000821}, {0.2999469, 0.9987899, 0.000126662, 0.0000694}, {0.2999469, 1.049146, 0.000182039, 0.000087}, {0.2999469, 1.100007, 0.000243545, 0.0000985}, {0.2999469, 1.151003, 0.000167506, 0.0000907}, {0.2999469, 1.20088, 0.000221046, 0.000117207}, {0.2999469, 1.24981, 0.000266948, 0.000130003}, {0.2999469, 1.298876, 0.000361939, 0.000171356}, {0.2999469, 1.35012, 0.000423017, 0.000222659}, {0.2999469, 1.400843, 0.000497565, 0.000299089}, {0.2999469, 1.45113, 0.000841964, 0.00069896}, {0.2999469, 1.487999, 0.001636413, 0.001292695}, {0.351399, 0.01203211, 0.1023983, 0.001765024}, {0.351399, 0.04910681, 0.02760775, 0.000890958}, {0.351399, 0.09977061, 0.001013449, 0.000120122}, {0.351399, 0.1508783, 0.000314347, 0.0000681}, {0.351399, 0.2008796, 0.000218643, 0.0000587}, {0.351399, 0.2510364, 0.000145264, 0.0000501}, {0.351399, 0.3009251, 0.0000988, 0.0000431}, {0.351399, 0.3508747, 0.0000886, 0.0000424}, {0.351399, 0.3999321, 0.000078, 0.0000407}, {0.351399, 0.4489179, 0.000113312, 0.0000492}, {0.351399, 0.5002585, 0.0000947, 0.0000463}, {0.351399, 0.5509165, 0.000150304, 0.0000649}, {0.351399, 0.6011173, 0.000443105, 0.000115168}, {0.351399, 0.6498302, 0.000857112, 0.000160557}, {0.351399, 0.6988636, 0.001158728, 0.000179657}, {0.351399, 0.7499531, 0.001562672, 0.000200422}, {0.351399, 0.8010127, 0.001445169, 0.000188441}, {0.351399, 0.8507249, 0.000932427, 0.0001463}, {0.351399, 0.9009042, 0.00044006, 0.00010092}, {0.351399, 0.9499643, 0.000182093, 0.00007}, {0.351399, 0.9987899, 0.000100358, 0.0000596}, {0.351399, 1.049146, 0.000133863, 0.0000725}, {0.351399, 1.100007, 0.000144129, 0.000072}, {0.351399, 1.151003, 0.00010871, 0.0000655}, {0.351399, 1.20088, 0.000123393, 0.0000805}, {0.351399, 1.24981, 0.000193871, 0.000102966}, {0.351399, 1.298876, 0.000241517, 0.000134903}, {0.351399, 1.35012, 0.000296181, 0.000181252}, {0.351399, 1.400843, 0.00026523, 0.000220609}, {0.351399, 1.45113, 0.000646058, 0.000572446}, {0.351399, 1.487999, 0.000963321, 0.000939469}, {0.4027665, 0.01203211, 0.09461402, 0.001366129}, {0.4027665, 0.04910681, 0.0254652, 0.000706637}, {0.4027665, 0.09977061, 0.001031896, 0.0000992}, {0.4027665, 0.1508783, 0.000384627, 0.0000604}, {0.4027665, 0.2008796, 0.000268799, 0.0000534}, {0.4027665, 0.2510364, 0.000208381, 0.0000464}, {0.4027665, 0.3009251, 0.000199062, 0.0000445}, {0.4027665, 0.3508747, 0.000186287, 0.0000418}, {0.4027665, 0.3999321, 0.000159836, 0.0000416}, {0.4027665, 0.4489179, 0.000107729, 0.000037}, {0.4027665, 0.5002585, 0.0000923, 0.0000347}, {0.4027665, 0.5509165, 0.0000702, 0.0000317}, {0.4027665, 0.6011173, 0.000146609, 0.0000496}, {0.4027665, 0.6498302, 0.000280341, 0.0000714}, {0.4027665, 0.6988636, 0.000459356, 0.0000931}, {0.4027665, 0.7499531, 0.000744988, 0.00011817}, {0.4027665, 0.8010127, 0.001140008, 0.000143582}, {0.4027665, 0.8507249, 0.001200483, 0.000141774}, {0.4027665, 0.9009042, 0.000922343, 0.000119712}, {0.4027665, 0.9499643, 0.000375711, 0.0000757}, {0.4027665, 0.9987899, 0.000140653, 0.0000492}, {0.4027665, 1.049146, 0.000098, 0.0000461}, {0.4027665, 1.100007, 0.0000772, 0.0000404}, {0.4027665, 1.151003, 0.0000815, 0.0000407}, {0.4027665, 1.20088, 0.0000899, 0.0000479}, {0.4027665, 1.24981, 0.0000992, 0.0000589}, {0.4027665, 1.298876, 0.000142484, 0.0000848}, {0.4027665, 1.35012, 0.000189181, 0.000109538}, {0.4027665, 1.400843, 0.000172183, 0.000138258}, {0.4027665, 1.45113, 0.000275446, 0.000293852}, {0.4027665, 1.487999, 0.000381214, 0.000439755}, {0.4496463, 0.01203211, 0.1094655, 0.001215262}, {0.4496463, 0.04910681, 0.03120829, 0.000643984}, {0.4496463, 0.09977061, 0.001421187, 0.0000962}, {0.4496463, 0.1508783, 0.000589879, 0.0000633}, {0.4496463, 0.2008796, 0.000401797, 0.0000524}, {0.4496463, 0.2510364, 0.000392448, 0.0000514}, {0.4496463, 0.3009251, 0.000374653, 0.0000495}, {0.4496463, 0.3508747, 0.000443615, 0.0000546}, {0.4496463, 0.3999321, 0.000371195, 0.0000521}, {0.4496463, 0.4489179, 0.000203434, 0.0000406}, {0.4496463, 0.5002585, 0.000117548, 0.0000317}, {0.4496463, 0.5509165, 0.0000764, 0.000026}, {0.4496463, 0.6011173, 0.0000956, 0.0000299}, {0.4496463, 0.6498302, 0.000120406, 0.0000352}, {0.4496463, 0.6988636, 0.000175619, 0.000043}, {0.4496463, 0.7499531, 0.000325115, 0.0000604}, {0.4496463, 0.8010127, 0.0005661, 0.0000836}, {0.4496463, 0.8507249, 0.000928296, 0.000105136}, {0.4496463, 0.9009042, 0.001128707, 0.000111962}, {0.4496463, 0.9499643, 0.000719185, 0.0000871}, {0.4496463, 0.9987899, 0.000239313, 0.0000504}, {0.4496463, 1.049146, 0.0000817, 0.0000313}, {0.4496463, 1.100007, 0.0000617, 0.0000287}, {0.4496463, 1.151003, 0.0000532, 0.0000284}, {0.4496463, 1.20088, 0.0000802, 0.0000369}, {0.4496463, 1.24981, 0.000094, 0.0000454}, {0.4496463, 1.298876, 0.00010737, 0.0000566}, {0.4496463, 1.35012, 0.0000915, 0.0000647}, {0.4496463, 1.400843, 0.00016223, 0.000102268}, {0.4496463, 1.45113, 0.000256105, 0.000193461}, {0.4496463, 1.487999, 0.000406342, 0.000335206}, {0.4967034, 0.01203211, 0.1515964, 0.001494316}, {0.4967034, 0.04910681, 0.03684591, 0.000740697}, {0.4967034, 0.09977061, 0.001324794, 0.000099}, {0.4967034, 0.1508783, 0.000433766, 0.0000559}, {0.4967034, 0.2008796, 0.000275803, 0.0000457}, {0.4967034, 0.2510364, 0.000212638, 0.0000404}, {0.4967034, 0.3009251, 0.000196184, 0.0000388}, {0.4967034, 0.3508747, 0.000205123, 0.0000397}, {0.4967034, 0.3999321, 0.000232467, 0.0000434}, {0.4967034, 0.4489179, 0.000401981, 0.0000576}, {0.4967034, 0.5002585, 0.000176261, 0.0000392}, {0.4967034, 0.5509165, 0.0000896, 0.0000293}, {0.4967034, 0.6011173, 0.0000941, 0.0000303}, {0.4967034, 0.6498302, 0.000100446, 0.0000324}, {0.4967034, 0.6988636, 0.000110629, 0.0000342}, {0.4967034, 0.7499531, 0.000192725, 0.0000444}, {0.4967034, 0.8010127, 0.000359514, 0.0000619}, {0.4967034, 0.8507249, 0.000674937, 0.0000873}, {0.4967034, 0.9009042, 0.001039717, 0.000108854}, {0.4967034, 0.9499643, 0.000770872, 0.0000938}, {0.4967034, 0.9987899, 0.000225213, 0.0000509}, {0.4967034, 1.049146, 0.0000582, 0.000027}, {0.4967034, 1.100007, 0.0000442, 0.0000254}, {0.4967034, 1.151003, 0.0000482, 0.0000287}, {0.4967034, 1.20088, 0.0000665, 0.0000361}, {0.4967034, 1.24981, 0.0000707, 0.0000395}, {0.4967034, 1.298876, 0.0000618, 0.0000412}, {0.4967034, 1.35012, 0.0000937, 0.0000635}, {0.4967034, 1.400843, 0.000150926, 0.0000974}, {0.4967034, 1.45113, 0.000135016, 0.000147398}, {0.4967034, 1.487999, 0.000233144, 0.000242054}, {0.5504108, 0.01203211, 0.09064252, 0.0014725}, {0.5504108, 0.04910681, 0.02602461, 0.000745193}, {0.5504108, 0.09977061, 0.000835608, 0.0000957}, {0.5504108, 0.1508783, 0.000236157, 0.0000513}, {0.5504108, 0.2008796, 0.000142981, 0.0000427}, {0.5504108, 0.2510364, 0.000107481, 0.0000387}, {0.5504108, 0.3009251, 0.0000878, 0.0000356}, {0.5504108, 0.3508747, 0.0000884, 0.0000348}, {0.5504108, 0.3999321, 0.000127604, 0.0000402}, {0.5504108, 0.4489179, 0.000139343, 0.0000394}, {0.5504108, 0.5002585, 0.000122183, 0.0000388}, {0.5504108, 0.5509165, 0.0000747, 0.0000328}, {0.5504108, 0.6011173, 0.0000848, 0.0000356}, {0.5504108, 0.6498302, 0.000123968, 0.0000454}, {0.5504108, 0.6988636, 0.000148527, 0.0000523}, {0.5504108, 0.7499531, 0.000235699, 0.0000658}, {0.5504108, 0.8010127, 0.000372422, 0.0000797}, {0.5504108, 0.8507249, 0.000677797, 0.000105258}, {0.5504108, 0.9009042, 0.000967788, 0.000128001}, {0.5504108, 0.9499643, 0.000557506, 0.0000969}, {0.5504108, 0.9987899, 0.000136945, 0.0000475}, {0.5504108, 1.049146, 0.0000519, 0.0000324}, {0.5504108, 1.100007, 0.0000573, 0.0000335}, {0.5504108, 1.151003, 0.0000676, 0.0000375}, {0.5504108, 1.20088, 0.0000507, 0.0000342}, {0.5504108, 1.24981, 0.0000355, 0.0000311}, {0.5504108, 1.298876, 0.0000463, 0.0000433}, {0.5504108, 1.35012, 0.000113439, 0.0000779}, {0.5504108, 1.400843, 0.000125893, 0.0001}, {0.5504108, 1.45113, 0.000127608, 0.000143131}, {0.5504108, 1.487999, 0.000108575, 0.000174224}, {0.5999553, 0.01203211, 0.06634204, 0.001353167}, {0.5999553, 0.04910681, 0.01829561, 0.000704955}, {0.5999553, 0.09977061, 0.000690618, 0.0000958}, {0.5999553, 0.1508783, 0.000167709, 0.0000499}, {0.5999553, 0.2008796, 0.000126736, 0.0000463}, {0.5999553, 0.2510364, 0.0000828, 0.0000358}, {0.5999553, 0.3009251, 0.0000879, 0.0000358}, {0.5999553, 0.3508747, 0.0000923, 0.0000381}, {0.5999553, 0.3999321, 0.0000769, 0.0000375}, {0.5999553, 0.4489179, 0.0000776, 0.0000401}, {0.5999553, 0.5002585, 0.0000767, 0.0000387}, {0.5999553, 0.5509165, 0.0000877, 0.0000394}, {0.5999553, 0.6011173, 0.000166282, 0.0000555}, {0.5999553, 0.6498302, 0.000232257, 0.0000684}, {0.5999553, 0.6988636, 0.000360469, 0.0000907}, {0.5999553, 0.7499531, 0.00039869, 0.000098}, {0.5999553, 0.8010127, 0.00053909, 0.00010748}, {0.5999553, 0.8507249, 0.000729154, 0.000115996}, {0.5999553, 0.9009042, 0.000611591, 0.000102393}, {0.5999553, 0.9499643, 0.000244657, 0.000068}, {0.5999553, 0.9987899, 0.0000664, 0.0000389}, {0.5999553, 1.049146, 0.0000428, 0.0000316}, {0.5999553, 1.100007, 0.0000545, 0.0000332}, {0.5999553, 1.151003, 0.0000771, 0.0000403}, {0.5999553, 1.20088, 0.0000709, 0.0000418}, {0.5999553, 1.24981, 0.000079, 0.0000527}, {0.5999553, 1.298876, 0.0000836, 0.0000684}, {0.5999553, 1.35012, 0.000146739, 0.0000985}, {0.5999553, 1.400843, 0.000180494, 0.000125324}, {0.5999553, 1.45113, 0.000171035, 0.000194538}, {0.5999553, 1.487999, 0.000283511, 0.000326393}, {0.6503139, 0.01203211, 0.08897097, 0.002566025}, {0.6503139, 0.04910681, 0.02465827, 0.001434306}, {0.6503139, 0.09977061, 0.000902531, 0.00018245}, {0.6503139, 0.1508783, 0.00021565, 0.0000701}, {0.6503139, 0.2008796, 0.000186667, 0.0000717}, {0.6503139, 0.2510364, 0.000151591, 0.0000644}, {0.6503139, 0.3009251, 0.000120543, 0.0000513}, {0.6503139, 0.3508747, 0.000108839, 0.0000451}, {0.6503139, 0.3999321, 0.0000846, 0.0000418}, {0.6503139, 0.4489179, 0.000115256, 0.0000494}, {0.6503139, 0.5002585, 0.000128018, 0.0000502}, {0.6503139, 0.5509165, 0.000132044, 0.0000477}, {0.6503139, 0.6011173, 0.000235156, 0.0000634}, {0.6503139, 0.6498302, 0.000448416, 0.0000941}, {0.6503139, 0.6988636, 0.000524899, 0.000111871}, {0.6503139, 0.7499531, 0.000584105, 0.000120938}, {0.6503139, 0.8010127, 0.000550121, 0.000109041}, {0.6503139, 0.8507249, 0.000462607, 0.000095}, {0.6503139, 0.9009042, 0.000262414, 0.0000695}, {0.6503139, 0.9499643, 0.000116691, 0.000049}, {0.6503139, 0.9987899, 0.0000866, 0.0000478}, {0.6503139, 1.049146, 0.0000572, 0.0000395}, {0.6503139, 1.100007, 0.0000328, 0.0000283}, {0.6503139, 1.151003, 0.0000645, 0.0000398}, {0.6503139, 1.20088, 0.0000764, 0.0000465}, {0.6503139, 1.24981, 0.0000914, 0.0000615}, {0.6503139, 1.298876, 0.000131544, 0.0000916}, {0.6503139, 1.35012, 0.000152969, 0.000107919}, {0.6503139, 1.400843, 0.000160366, 0.000125925}, {0.6503139, 1.45113, 0.000227675, 0.000244772}, {0.6503139, 1.487999, 0.000410726, 0.000420443}, {0.6990286, 0.01203211, 0.1305426, 0.004546241}, {0.6990286, 0.04910681, 0.03146357, 0.002106031}, {0.6990286, 0.09977061, 0.001037019, 0.00026412}, {0.6990286, 0.1508783, 0.000231548, 0.000091}, {0.6990286, 0.2008796, 0.000298593, 0.000118439}, {0.6990286, 0.2510364, 0.000231503, 0.000103976}, {0.6990286, 0.3009251, 0.000136526, 0.0000669}, {0.6990286, 0.3508747, 0.000123731, 0.0000975}, {0.6990286, 0.3999321, 0.000157325, 0.000139099}, {0.6990286, 0.4489179, 0.000276389, 0.000156038}, {0.6990286, 0.5002585, 0.000241361, 0.000137575}, {0.6990286, 0.5509165, 0.000154788, 0.0000892}, {0.6990286, 0.6011173, 0.000268714, 0.0000745}, {0.6990286, 0.6498302, 0.000475129, 0.000104437}, {0.6990286, 0.6988636, 0.000607848, 0.000120112}, {0.6990286, 0.7499531, 0.000470629, 0.00011044}, {0.6990286, 0.8010127, 0.000318165, 0.0000894}, {0.6990286, 0.8507249, 0.000204583, 0.0000658}, {0.6990286, 0.9009042, 0.000127872, 0.0000515}, {0.6990286, 0.9499643, 0.0000904, 0.0000453}, {0.6990286, 0.9987899, 0.000180306, 0.0000659}, {0.6990286, 1.049146, 0.000121658, 0.000054}, {0.6990286, 1.100007, 0.000130731, 0.000056}, {0.6990286, 1.151003, 0.00015566, 0.0000637}, {0.6990286, 1.20088, 0.000097, 0.0000527}, {0.6990286, 1.24981, 0.0000895, 0.0000586}, {0.6990286, 1.298876, 0.00014314, 0.0000869}, {0.6990286, 1.35012, 0.000181547, 0.000118287}, {0.6990286, 1.400843, 0.000167488, 0.000131239}, {0.6990286, 1.45113, 0.000292798, 0.000288394}, {0.6990286, 1.487999, 0.000433997, 0.000458083}, {0.7477285, 0.3009251, 0.000053, 0.0000462}, {0.7477285, 0.3508747, 0.0000956, 0.000133103}, {0.7477285, 0.3999321, 0.000344739, 0.000279699}, {0.7477285, 0.4489179, 0.000390532, 0.000270478}, {0.7477285, 0.5002585, 0.000392541, 0.000259302}, {0.7477285, 0.5509165, 0.000149147, 0.000128412}, {0.7477285, 0.6011173, 0.000165453, 0.0000795}, {0.7477285, 0.6498302, 0.000452263, 0.000147439}, {0.7477285, 0.6988636, 0.000415388, 0.000125599}, {0.7477285, 0.7499531, 0.000297813, 0.000243738}, {0.7477285, 0.8010127, 0.000194161, 0.000304051}, {0.7477285, 0.8507249, 0.000154568, 0.00027359}, {0.7477285, 0.9009042, 0.000134434, 0.000251633}, {0.7477285, 0.9499643, 0.000110127, 0.00019129}, {0.7477285, 0.9987899, 0.000110382, 0.00010382}, {0.7477285, 1.049146, 0.000129385, 0.0000827}, {0.7477285, 1.100007, 0.000353017, 0.0000981}, {0.7477285, 1.151003, 0.000538544, 0.00013636}, {0.7477285, 1.20088, 0.00015782, 0.0000889}, {0.7477285, 1.24981, 0.0000696, 0.0000608}, {0.7477285, 1.298876, 0.000146578, 0.00013496}, {0.7477285, 1.35012, 0.000300833, 0.000205088}, {0.7477285, 1.400843, 0.000445233, 0.000245628}, {0.7477285, 1.45113, 0.000371585, 0.000403792}, {0.7477285, 1.487999, 0.00069879, 0.000703723}, {0.79343, 0.8010127, 0.000545414, 0.000697371}, {0.79343, 0.8507249, 0.000225278, 0.000428143}, {0.79343, 0.9009042, 0.000404924, 0.000554523}, {0.79343, 0.9499643, 0.000148193, 0.000297461}, {0.79343, 0.9987899, 0.000165649, 0.000213896}, {0.79343, 1.049146, 0.0000836, 0.000110634}, {0.79343, 1.100007, 0.000175279, 0.0000915}, {0.79343, 1.151003, 0.000331701, 0.000166089}, {0.79343, 1.20088, 0.000197516, 0.000136657}, {0.79343, 1.24981, 0.0000473, 0.0000663}, {0.79343, 1.298876, 0.000169997, 0.000187402}, {0.79343, 1.35012, 0.000461569, 0.000344723}, {0.79343, 1.400843, 0.000334411, 0.000273181}, {0.79343, 1.45113, 0.000547673, 0.000501559}, {0.79343, 1.487999, 0.000890756, 0.000845645}, {0.8292615, 1.35012, 0.000118945, 0.000182641}, {0.8292615, 1.400843, 0.000102903, 0.000170622}, {0.8292615, 1.45113, 0.000157944, 0.000294485}, {0.8292615, 1.487999, 0.000248875, 0.000441169}} 

My model yields the energy at a specific coordinate $ \boldsymbol{k} =\{k_x, k_y, k_z\}$ where $ \boldsymbol{k} = x(\boldsymbol{b}_1 + \boldsymbol{b}_2)$ . Here $ x$ is the first entry of each quadruple in the dataset, $ \boldsymbol{b}_1 = \{ 2 \pi, 2\pi/\sqrt{3}, 0 \}$ , and $ \boldsymbol{b}_2 = \{ 0, 4\pi/\sqrt{3}, 0 \}$

(* First obtain the measured energy values and store them in a list *) ω = DeleteDuplicates@*Flatten@dataset[[All, 2]]; b1 = {2π, (2π)/Sqrt[3], 0}; b2 = {0, (4π)/Sqrt[3], 0}; xKtoM = DeleteDuplicates@*Flatten@dataset[[All, 1]]; k = Table[xKtoM[[i]] (b1 + b2), {i, 1, Length[xKtoM]}]; 

I then go on to define my model

(* Bohr magneton μ in units of eV*T^-1 pulled from wikipedia*) μ = 5.7883818012*10^-5;  (* This is the model where we have taken the positive branch of the energy spectrum *) d[kx_, ky_, kz_, g_, Bz_, Jx_, Jy_, Jz_] := {1/2 (Jx + Jy) (Cos[k[[1]]] + Cos[k[[2]]] + Cos[k[[1]] + k[[2]]]) - 3 Jz + g \[Mu] Bz,  1/2 (Jx - Jy) (E^(-I 2 \[Pi]/3) Cos[k[[1]]] + E^(I 2 \[Pi]/3) Cos[k[[2]]] + Cos[k[[1]] + k[[2]]])};  spectrum[{kx_, ky_, kz_}] := Norm[d[kx, ky, kz, g, 4, Jx, Jy, Jz]]; (* Get the spectrum going from the high symmetry K \[Rule] M path using the k vector/list we defined above. This is the model we use for the dataset *) model = Map[spectrum, k]; 

From here I would have the energy values at 18 separate points if I had specified values for Jx, Jy, Jz, and g. I then thought to define a cost function that takes my model and subtracts the corresponding measured energy value and then try to find the minimum using the built-in FindMinimum function

(* Define a cost function between the model and the measured energy values Subscript[\[Omega], i] *) CostFunction[Jx_, Jy_, Jz_, g_] := Sum[Abs[model[[i]] - ω[[i]]]^2, {i, 1, Length[ω]}] (* Minimize this cost function to attempt to extract the parameters Jx, Jy, Jz, and g *) params = FindMinimum[model, {{Jx, 0.5}, {Jy, 0.5}, {Jz, 0.5}, {g, 2}}] 

My only issue with this is that

  1. My model is a list of functions while the measured energy values $ \omega$ is a list of real numbers
  2. Using FindMinimum yields quite a lot of errors

Is it possible to get around these issues using something like NonLinearModelFit or something similar? Let me know if I should clarify anything or add any additional info and thanks in advance!

Fitting an integral function given a set of data points

I have a set of measures of the resistivity of a given material at different thicknesses and I’m trying to fit them using the Fuchs-Sondheimer model. My code is:

data = {{8.1, 60.166323}, {8.5, 47.01784}, {14, 52.534961}, {15,     50.4681111501753}, {20, 39.0704975714401}, {30,     29.7737879177201}, {45, 22.4406}, {50, 15.2659673601299}, {54,     18.189933218482}, {73, 14.8377093467966}, {100,     15.249523361101}, {137, 15.249523361101}, {170,     10.7190970441753}, {202, 15.249523361101}, {230, 10.9744085456615}}  G[d_, l_, p_] := NIntegrate[(y^(-3) - y^(-5)) (1 - Exp[-yd/l])/(1 - pExp[-yd/l]), {y,0.01, 1000}];  nlm  = NonlinearModelFit[data, 1/(1 - (3 l/(2 d)) G [d, l, p]) , {{l, 200}, {p, 4}}, d, Method -> NMinimize] 

However it returns me these errors:

NIntegrate::inumr: The integrand ((1-E^(-(yd/l))) (-(1/y^5)+1/y^3))/(1-pExp[-(yd/l)]) has evaluated to non-numerical values for all sampling points in the region with boundaries {{0.01,1000}}. 
NonLinearModelFit: the function value is not a real number at {l,p} = {200.,4.} 

I think that the problem is in the way in which I defined the integral function G[d, l, p], because I had to fit a different set of data points with a different function of only one variable which I defined through the NIntegrate function and it gave me no error. Could anyone please help me?

Fitting plot and data to an equation

If I have the following data:

data={{2, 66.7635}, {Log[300]/Log[10], 69.9679}, {Log[600]/Log[10],    71.54}, {3, 72.2428}, {-2.30103, 54.0023}, {-(Log[60]/Log[10]),    55.1941}, {-(Log[20]/Log[10]), 56.0038}, {-1,    56.9497}, {-(Log[6]/Log[10]), 57.305}, {-(Log[10/3]/Log[10]),    57.7213}, {-(Log[2]/Log[10]), 58.2489}, {-2.30103,    54.0367}, {-(Log[60]/Log[10]), 55.1157}, {-(Log[20]/Log[10]),    56.1704}, {-1, 56.7117}, {-(Log[6]/Log[10]),    57.2506}, {-(Log[10/3]/Log[10]), 57.7097}, {-(Log[2]/Log[10]),    58.1068}} 

Which looks like this plotted:

enter image description here

I have two questions:

1) How can I fit and plot the fit of this data based on the following equation?

: `` where Tf'_ref=57.2506 , q_ref=0.166667 and c1 and c2 are the fitting parameters. Also, notice that data is Tf' vs Log q in the equation.

2) How can I find the values of c1 and c2 which are the fitting parameters.

The fitting (orange line) is supposed to look like this (done in excel):

enter image description here

EDIT: I tried using NonLinearFitModel like this: Table[{NonlinearModelFit[data, Logqref - ((c1*(data[[i, 2]] - Tfref))/(c2*(data[[i, 2]] - Tfref))), {{c1, 8.6}, {c2, 17.2}}, x]; }, {i, 1, 11}] but this does not work. The reason I tried this is because data[[i, 2]] represents Tf' in the equation. Here Logref=Log10[0.16667]

Fitting Experimental Data To SRK-Type Equation of State. Minimization

I’m trying to find parameters to fit an EoS to saturation pressures to different temperatures.

My experimental data are like this

psatx={{Temperature1,Pressure1,Uncertainty1},{T2,p2,u2},....} 

Then I defined a function to calculate saturation pressures

psat[T_, p0_, Tc_, a0_, b_, c1_, E11r_, v11_] := (Do[    p[0] = p0;    f11 = Exp[-E11r/T] - 1;    m11 = v11*f11;    a = a0*(1 + c1*(1 - Sqrt[T/Tc]))^2;    \[Alpha] = p[i]*a/(R*T)^2; (* Dimensionless groups*)    \[Beta] = p[i]*b/R/T;    \[Gamma] = p[i]*m11/R/T;    d0 = -\[Gamma]*\[Beta]*(\[Beta] + \[Alpha]);(*Coefficients of the equation*)    d1 = \[Alpha]*(\[Gamma] - \[Beta]) - \[Beta]*\[Gamma]*(1 + \[Beta]);    d2 = \[Alpha] - \[Beta]*(1 + \[Beta]);    d3 = \[Gamma] - 1;    d4 = 1;    polin = d4*z^4 + d3*z^3 + d2*z^2 + d1*z + d0;    Raices = NSolve[polin == 0, z, PositiveReals]; (* Solving the 4th grade polinomy for compressibility factor*)    zv = Max[z /. Raices];    zl = Min[z /. Raices];    vv = zv*R*T/p[i];    vl = zl*R*T/p[i];    ln\[CapitalPhi]v =      zv - 1 - Log[zv] + Log[vv/(vv - b)] + a/b/R/T*Log[vv/(vv + b)] +       Log[vv/(vv + m11)]; (*Fugacity coefficients*)    ln\[CapitalPhi]l =      zl - 1 - Log[zl] + Log[vl/(vl - b)] + a/b/R/T*Log[vl/(vl + b)] +       Log[vl/(vl + m11)];    \[CapitalPhi]v = Exp[ln\[CapitalPhi]v];    \[CapitalPhi]l = Exp[ln\[CapitalPhi]l];    p[i + 1] = p[i]*\[CapitalPhi]l/\[CapitalPhi]v,    {i, 0, 9}];   p[9])  

Where T is the temperature, p0 is the initial guess for pressure, Tc is the critical temperature and a0, b, c1, E11r, v11 are the equation’s parameters.

Up to this point, we have a saturation pressure calculator, given the parameters, and it works just fine, now the thing that I can’t seem to solve is fitting it to my experimental data, by minimizing an objective function, which is:

enter image description here

I declared it like this:

F[a0_, b_, c1_, E11r_, v11_] :=   Sum[(psat[psatx[[k, 1]], psatx[[k, 2]], Tcaceto, a0, b, c1, E11r,        v11] - psatx[[k, 2]])^2/psatx[[k, 3]]^2, {k, 200}]; (* I declared the Tc as "Tcaceto", a constant, and I use as initial guess for each psat calculation the experimental pressure*) 

And then I just used NMinimize, in this way.

NMinimize[F[a0, b, c1, E11r, v11], {a0, b, c1, E11r, v11}] 

I run it, and it just never finishes. I don’t know what could be the thing that doesn’t work, I’ve tried setting the method, starting points, but the result is the same. I would really apreciate if someone helped me in this matter. Thanks.

Chi^2 fitting for correlated data

Suppose you have $ N$ correlated data points $ \vec{y}_\mathrm{data}$ and a model that is a function of $ M$ parameters $ \vec{x}$ . The associated $ \chi^2$ statistic is

$ \chi^2 = (\vec{y}_\mathrm{data} – \vec{y}_\mathrm{theo}(\vec{x}) \cdot C^{-1} \cdot (\vec{y}_\mathrm{data} – \vec{y}_\mathrm{theo}(\vec{x}))$ ,

where $ \vec{y}_\mathrm{data}$ is the vector with the data points, $ \vec{y}_{theo}(\vec{x})$ is the fit function and $ C$ is the covariance matrix associated the data points. To best fit the model, one minimizes $ \chi^2$ with respect to $ \vec{x}$ .

What is the best function on Mathematica to do this? NonlinearModelFit doesn’t handle correlated data and FindMinimum doesn’t provide useful statistics (like the covariance matrix associated with $ \vec{x}$ ).

why ODE Fitting is not producing a flattened curve?

I have fitted parameter of an ODE with experimental data. Though the fit is very good in the start (up to {10, 0.004048}) but then it does not flatten as the experimental data does. Could you please suggest if I need to do anything to get a better fit.

sddata = {{0, 0.017622}, {1, 0.016368}, {2, 0.014476}, {3, 0.012254}, {4, 0.008536}, {5, 0.006996}, {10, 0.004048}, {20, 0.003454}, {40, 0.003432}, {60, 0.003234}}; eqns = {sd'[t] == -k1 sd[t]}; aa[t_] = DSolveValue[{eqns, sd[0] == 0.017622}, {sd[t]}, t] model[k1_] := Sum[(aa[sddata[[i, 1]]] - sddata[[i, 2]])^2, {i, Length@sddata}] NMinimize[model[k1], {k1}] 

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Are neural network latent representations fitting a Gaussian distribution?

Neural network latent (or pre-activation) representations are often fitting a Gaussian-like bell distribution:

Preactivation Gaussian distribution (image source)

The representations are weighted sums of inputs to the neurons. Within a layer, before batch distribution, it would be interesting to know if the pre-activations are distributed in a particular way.

My question is about finding any explanation or mention of this observation in the literature. Is there any reference in the literature supporting this, or explaining what a non-Gaussian-like distribution indicates?

Is this hombrew barbarian subclass balanced and fitting for a “thug” barbarian

At level 3 you can roll with the punches. As a reaction when damaged you can generate temporary health = prof +con which will disappear at the end of the round

At level 3 you may be the muscle of the group but sometimes you’re just there to show who you don’t want to be on the bad side of. you and allies with you around have advantage on insight, persuasion, intimidation checks on creatures that have a challenge ratings less then or equal to half your overall level

At level 6: your blows send your foes reeling. after landing a reckless attack the enemy must make a con save dc 8 + str + prof bonus or be stunned till the start of your next turn

At level 10 “is that all you got” spits out bloody tooth you can add your con mod to death saving throws and your allowed one reroll but you must use the new roll and stabilizing you will bring you up to con hp

At level 14 as a reaction when below half hit point choose one creature you can see within 10 ft and they must make a wisdom saving throw (dc= 8+cha+prof) or be frightened of you till they leave the radius or break line of sight where they will remake the saving throw. While raging this affects all enemies within 15 ft

Fitting a polynomial to a set of points or to a skeleton


Available data

Available to me is a set of points which can be represented as shown in image 1:

Original data

Also available to me is a non-continuous path derived from this data. It is not important how this non-continuous path is obtained. It is however important, that it roughly represents a curve I intent to approximate. This non-continuous path is shown in image 2:

Non-continuous path derived from original data

Goal

I want to approximate this data using a polynomial of either second or third degree. Examples of these approximations are shown in images 3, 4:

Fit curve to original data

Fit curve to non-continuous path

Problem / question

Now I am looking for a way to obtain the red curve. Some details confuse me, where my knowledge is likely to be simply lacking. For example, how to fit a polynomial, when technically what I require is not a function, at least not in this coordinate system, because there will be situations where an x value is being assigned two y values.

I thought of possibly using the ends of my path to define a new x-axis, but I consider this approach faulty. Another consideration are Splines.

How should I go about obtaining this red curve from the non-continuous path (preferred) or from original data? What sources should I look into?

Apologies if this is an already answered question which I suspect it might be. However I have been issuing search queries for this without success, hence my question.