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Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions

์ž‘์„ฑ์ž
  • Haebom
์นดํ…Œ๊ณ ๋ฆฌ
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์ €์ž

Ha Dang, Sebastian Schmidt, Juergen Hesser

๐Ÿ’ก ๊ฐœ์š”

์‹ ๊ฒฝ๋ง ์—ฐ์‚ฐ์ž(Neural Operator)๋Š” ํŽธ๋ฏธ๋ถ„ ๋ฐฉ์ •์‹(PDE)์˜ ํ•ด ์—ฐ์‚ฐ์ž๋ฅผ ํ•™์Šตํ•˜๋Š” ๋ฐ ๋›ฐ์–ด๋‚œ ์„ฑ๋Šฅ์„ ๋ณด์—ฌ์™”์ง€๋งŒ, ๋ณธ์งˆ์ ์œผ๋กœ ์—ฐ์†์ ์ธ ํ‘œํ˜„ ๋ฐฉ์‹์œผ๋กœ๋Š” ๋ถˆ์—ฐ์†์„ฑ๊ณผ ๊ธ‰๊ฒฉํ•œ ๋ณ€ํ™”๋ฅผ ํฌ์ฐฉํ•˜๋Š” ๋ฐ ์–ด๋ ค์›€์ด ์žˆ์Šต๋‹ˆ๋‹ค. ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์ด๋Ÿฌํ•œ ๋ถˆ์—ฐ์†์„ฑ์„ ๋ช…์‹œ์ ์œผ๋กœ ๋ชจ๋ธ๋งํ•˜๊ณ  ํ•™์Šต ๋ณต์žก์„ฑ์„ ์ค„์ด๋Š” 2๋‹จ๊ณ„ ํ•™์Šต ํ”„๋ ˆ์ž„์›Œํฌ์ธ Cut-DeepONet์„ ์ œ์•ˆํ•ฉ๋‹ˆ๋‹ค. Cut-DeepONet์€ ์˜์—ญ์„ ๋งค๋„๋Ÿฌ์šด ํ•˜์œ„ ์˜์—ญ์œผ๋กœ ๋ถ„ํ• ํ•˜๊ณ  ๋ถˆ์—ฐ์†์„ฑ์„ ๊ณ ์ฐจ์› ๊ณต๊ฐ„์˜ ๊ฒฝ๊ณ„๋กœ ํ‘œํ˜„ํ•˜๋Š” ๋ฆฌํ”„ํŒ… ์ „๋žต์„ ํ†ตํ•ด ๋ฌธ์ œ๋ฅผ ์žฌ์ •๋ฆฝํ•ฉ๋‹ˆ๋‹ค.

๐Ÿ”‘ ์‹œ์‚ฌ์  ๋ฐ ํ•œ๊ณ„

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์‹ ๊ฒฝ๋ง ์—ฐ์‚ฐ์ž์˜ ๋ถˆ์—ฐ์†์„ฑ ๋ฐ ๊ธ‰๊ฒฉํ•œ ๋ณ€ํ™” ์ฒ˜๋ฆฌ ๋Šฅ๋ ฅ ํ–ฅ์ƒ
โ€ข
๋‚ฎ์€ ํ•ด์ƒ๋„์˜ ๋ฐ์ดํ„ฐ๋กœ๋„ ๊ธฐ์กด ์ตœ์ฒจ๋‹จ ๋ฐฉ๋ฒ•๋ก ์„ ๋Šฅ๊ฐ€ํ•˜๋Š” ์„ฑ๋Šฅ ๋‹ฌ์„ฑ
โ€ข
๋ชจ๋ธ ๋ณต์žก์„ฑ์„ ๋Š˜๋ฆฌ๋Š” ๋Œ€์‹  ์—ฐ์‚ฐ์ž ํ•™์Šต์˜ ํ‘œํ˜„ ๋ฐฉ์‹์„ ๋ณ€๊ฒฝํ•˜๋Š” ๊ฒƒ์ด ํšจ๊ณผ์ ์ž„์„ ์ž…์ฆ
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์ถ”๊ฐ€์ ์ธ ๋„คํŠธ์›Œํฌ๊ฐ€ ๋ถˆ์—ฐ์† ์œ„์น˜๋ฅผ ์˜ˆ์ธกํ•ด์•ผ ํ•˜๋Š” ์˜ค๋ฒ„ํ—ค๋“œ ๋ฐœ์ƒ
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