Criação de um algoritmo de aprendizagem profunda para detectar eventos inesperados de ondas gravitacionais
Desde a detecção direta de ondas gravitacionais em 2015, os cientistas têm se apoiado em um truque: eles só conseguem detectar as ondas que correspondem às previsões teóricas, o que é bem o oposto do que a ciência costuma fazer.
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)
O sinal de onda gravitacional recebido em um detector LIGO (laranja), sobreposto por previsões teóricas da relatividade geral (verde) e a aparência do sinal esperado no detector (azul). Crédito: Physics magazine, APS [https://physics.aps.org/articles/v9/52]
Desde a detecção direta de ondas gravitacionais em 2015, os cientistas têm se apoiado em um truque: eles só conseguem detectar as ondas que correspondem às previsões teóricas, o que é bem o oposto do que a ciência costuma fazer.
Agora, um grupo de físicos apresentou um modelo computacional que poderia capturar todas as ondas gravitacionais que passam pela Terra, em vez de apenas as esperadas. O artigo foi publicado no servidor de pré-impressão arXiv.
Décadas depois de Einstein descobrir que sua teoria geral da relatividade previa ondas gravitacionais — ondulações viajantes no tecido do espaço-tempo — os físicos calcularam suas assinaturas esperadas para alguns cenários simples. Um deles foi a forma de onda passageira para fusões buraco negro-buraco negro, que foi a primeira onda detectada a partir de dados interferométricos recebidos em 14 de setembro de 2015. (O artigo não foi publicado até fevereiro do ano seguinte.)
Assumindo o evento que produziu as ondas, os cientistas gravitacionais foram capazes de prever o sinal exato que apareceria nas instalações interferométricas de laser de braço longo, como o LIGO (que tem duas unidades nos EUA), o VIRGO na Itália e vários outros ao redor do mundo.
Os observacionalistas precisavam saber o que esperar para treinar seus interferômetros sobre o que procurar, porque uma onda passageira só moveria os braços do interferômetro em um milésimo da largura de um próton. Ruído ambiental, até mesmo caminhões passando, poderia facilmente dar origem a movimento nos braços que tinham que ser filtrados para distinguir uma onda gravitacional real.
Cálculos também foram realizados para fusões de estrelas de nêutrons-buracos negros e fusões de estrelas de nêutrons-estrelas de nêutrons. Além disso, a assinatura de ondas gravitacionais contínuas produzidas por estrelas de nêutrons simétricas de rotação rápida e ondas gravitacionais estocásticas, por exemplo, do Big Bang, puderam ser obtidas dos dados. Usando esses modelos, mais de sete dúzias de eventos de ondas gravitacionais foram detectados no geral.
Mas esse método não detecta ondas gravitacionais que não aparecem na forma de uma das previsões conhecidas, conhecidas como "transitórios" ou "explosões de ondas gravitacionais", de eventos inesperados baseados em física diferente. Além disso, os métodos de detecção atuais são muito lentos.
Após a passagem de uma onda gravitacional, os astrônomos querem ser capazes de identificar rapidamente sua fonte para informar outros observatórios a procurar por quaisquer eventos eletromagnéticos ou de partículas da mesma fonte — o que é conhecido como astronomia multimensageira.
Radiação eletromagnética, incluindo luz visível , e neutrinos são esperados de certas atividades astrofísicas grandes e violentas, incluindo as usuais fusões de pares binários. Após a recepção de um possível trem de ondas gravitacionais, o processamento e a comunicação com outros instrumentos podem atualmente exigir centenas de unidades de processamento dedicadas e levar dezenas de segundos ou até minutos, muito lento para um aviso de "alerta".
Nos últimos anos, os físicos têm tentado melhorar as limitações da forma de onda usando redes neurais convolucionais (CNNs), um tipo de algoritmo especializado de aprendizado profundo, para evitar detectores treinados para reconhecer apenas certos eventos.
No entanto, até o momento, as CNNs que foram programadas ainda exigem um modelo preciso do sinal alvo para treinamento e, portanto, não notarão fontes inesperadas, como aquelas previstas do colapso do núcleo de supernovas e longas explosões de raios gama. Limites físicos e computacionais desconhecidos podem arruinar qualquer chance de detecção de multimensageiros.
Aqui, os pesquisadores definiram uma meta de usar um único processador e relatar eventos de ondas gravitacionais em cerca de um segundo. Eles desenvolveram uma arquitetura multicomponente onde uma CNN detecta transientes que são simultâneos em vários detectores enquanto uma segunda CNN procura correlação entre os detectores para eliminar ruído de fundo coincidente ou falhas.
Dessa forma, "nossa busca utiliza aprendizado de máquina e visa ajudar a apontar os telescópios 'tradicionais' em direção a tal fonte em questão de segundos", disse Vasileos Skliris do Gravity Exploration Institute na Escola de Física e Astronomia da Universidade de Cardiff, no País de Gales, Reino Unido. "Dessa forma, seremos capazes de extrair o máximo de informações que pudermos desses eventos inesperados."
A abordagem de aprendizado profundo do grupo era diferente dos métodos anteriores de uma maneira crucial: em vez de ensinar uma CNN a identificar formas de sinal específicas nos dados, eles criaram CNNs que podiam detectar consistência em intensidade e tempo entre dois ou mais fluxos de dados.
As CNNs foram então treinadas usando sinais simulados e rajadas de ruído aleatório que têm características semelhantes. Ao usar os mesmos padrões de forma de onda para os sinais e ruído, as CNNs foram impedidas de depender do padrão do sinal para tomar decisões; em vez disso, as CNNs aprendem a avaliar o quão bem os detectores concordam entre si, permitindo que seus modelos tenham a possibilidade de detecção em tempo real de transientes de ondas gravitacionais.
Como teste, eles executaram os dados observados nas duas primeiras execuções do LIGO e do VIRGO e encontraram boa concordância.
"Na década de 1960, as explosões de raios gama foram a nova surpresa astrofísica quando a astronomia de raios gama deu seus primeiros passos", disse Skliris. "A astronomia de ondas gravitacionais está na mesma idade inicial, e podemos ter um futuro emocionante pela frente."
Mais informações: Vasileios Skliris et al, Detecção em tempo real de transientes de ondas gravitacionais não modelados usando redes neurais convolucionais, arXiv (2020). DOI: 10.48550/arxiv.2009.14611
Informações do periódico: arXiv