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+have+shown+high+potential+in+their+ability+to+solve+complex+differential+equations.+One+example+is+the+use+of+PINNs+to+solve+the+gravity+field+modeling+problem+--+learning+convenient+representations+of+the+gravitational+potential+from+position+and+acceleration+data.+These+PINN+gravity+models%252C+or+PINN-GMs%252C+have+demonstrated+advantages+in+model+compactness%252C+robustness+to+noise%252C+and+sample+efficiency+when+compared+to+popular+alternatives%253B+however%252C+further+investigation+has+revealed+various+failure+modes+for+these+and+other+machine+learning+gravity+models+which+this+manuscript+aims+to+address.+Specifically%252C+this+paper+introduces+the+third+generation+Physics-Informed+Neural+Network+Gravity+Model+(PINN-GM-III)+which+includes+design+changes+that+solve+the+problems+of+feature+divergence%252C+bias+towards+low-altitude+samples%252C+numerical+instability%252C+and+extrapolation+error.+Six+evaluation+metrics+are+proposed+to+expose+these+past+pitfalls+and+illustrate+the+PINN-GM-III%27s+robustness+to+them.+This+study+concludes+by+evaluating+the+PINN-GM-III+modeling+accuracy+on+a+heterogeneous+density+asteroid%252C+and+comparing+its+performance+to+other+analytic+and+machine+learning+gravity+models.&cdnurl=https%3a%2f%2fth.bing.com%2fth%2fid%2fR.4f2f9b2bcb0c0f64efd35977d0316794%3frik%3d09sIDTpr8JPpJg%26pid%3dImgRaw%26r%3d0&exph=630&expw=1200&q=Model+Architecture+of+Physics+Informed+Neural+Network&FORM=IRPRST&ck=D2BCA9E463F9CACCC04A314DA7A4C09C&selectedIndex=5&itb=0)
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