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SUMMARY:The Philosophy of Learned Operators: a New Kind of Scientific Mode
 l - Conor Rowan
DTSTART;TZID=US/Central:20260717T093000
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DTSTAMP:20260726T083440Z
UID:pretalx-iacap-2026-JYXD9T@pretalx.iacapconf.org
DESCRIPTION:Engineering practice has historically relied on models grounde
 d in ordinary and partial differential equations (PDEs) to relate system i
 nputs\, such as forces\, fluxes\, or heat sources\, to observable outputs\
 , such as displacement\, concentration\, or temperature. These physics-bas
 ed models are interpretable and generalizable\, but they require deep doma
 in knowledge and significant computational resources. Scientific machine l
 earning (SciML)\, and in particular operator learning\, offers an alternat
 ive strategy to predictive modeling: neural networks trained directly on d
 ata to approximate the input-output relationship traditionally furnished b
 y PDEs. These learned operators can be highly accurate\, computationally e
 fficient\, and do not require mechanistic insight into the system under st
 udy\, but they lack interpretability and fail to make meaningful predictio
 ns when queried outside the training data.\n\nIn this paper\, we argue tha
 t learned operators constitute a novel kind of scientific model\, and are 
 under-theorized from a philosophical perspective. Unlike traditional pheno
 menological laws\, they attempt to entirely replace governing PDEs with hi
 gh-dimensional data-driven mappings. Drawing on work in the philosophy of 
 scientific explanation\, laws\, and models\, we examine how surrogate mode
 ls fit---or fail to fit---within existing philosophical frameworks. We arg
 ue that their limited scope\, opacity\, vulnerability to adversarial attac
 k\, and neglect of unobservable entities distinguish them from theory-base
 d models in epistemically significant ways. Additionally\, we suggest that
  new frameworks for verification and validation are required if learned op
 erators are to be safely integrated into scientific and engineering practi
 ce.
LOCATION:Apollo Auditorium
URL:https://pretalx.iacapconf.org/iacap-2026/talk/JYXD9T/
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